ML Course For Beginners 2026 | Machine Learning Tutorial | Machine Learning Roadmap | Edureka

Key Takeaways

from. Hello everyone and welcome to the machine learning course for beginners. In this course, [music] you will discover how machines learn from data to make predictions and decisions. The foundation of modern artificial intelligence. [music] We will start from the basics understanding what machine learning is, the types of machine learning models [music] and the mathematics behind them in an easy and practical way. You will then explore popular algorithms like linear regression, [music] logistic regression, decision trees and more, learning when and how to apply each one. [music] You will also get hands-on experience using Python and real world data sets, [music] helping you build your first predictive model stepby step. And by the end of this [music] course, you will have a strong foundation in machine learning concepts and the confidence to start your journey as a data or AI professional. So before we begin, please like, share and subscribe to Edureka's YouTube channel and hit the bell icon to stay [music] updated on the latest tech content from Edureka. Also check out IDUka's [music] post-graduate program in generative AI and machine learning in collaboration with Illinois Tech which offers a unique opportunity to explore the cuttingedge world of [music] generative AI and develop advanced AI covered solutions. [music] This program covers in demand topics including machine learning, deep learning, natural language processing, [music] prompt engineering, generative AI, LLM, RAG, agentic AI and [music] much more. Learn from industry experts through a curriculum built around real world hands-on use cases designed to equip you with the practical and job ready skills. Now let us get started by understanding what machine learning is. >> As you know we are living in a world of humans and machines. Humans have been evolving and learning from the past experience since millions of years. On the other hand, the era of machines and robots have just begun. In today's world, these machines or the robots are like they need to be programmed before they actually follow your instructions. But what if the machines started to learn on their own and this is where machine learning comes into picture. Machine learning is the core of many futuristic technological advancement in our world. Today you can see various examples or implementation of machine learning around us such as Tesla's self-driving car, Apple Siri, Sophia AI robot and many more are there. So what exactly is machine learning? Well, machine learning is a sub field of artificial intelligence that focuses on the design of system that can learn from and make decisions and predictions based on the experience which is data. In the case of machines, machine learning enables computer to act and make datadriven decisions rather than being explicitly programmed to carry out a certain task. These programs are designed to learn and improve over time when exposed to new data. Let's move on and discuss one of the biggest confusion of the people in the world. They think that all the three of them the AI, the machine learning and the deep learning all same. You know what? They are wrong. Let me clarify things for you. Artificial intelligence is a broader concept of machines being able to carry out task in a smarter way. It covers anything which enables the computer to behave like humans. Think of a famous Turing test to determine whether a computer is capable of thinking like a human being or not. If you're talking to Siri on your phone and you get an answer, you're already very close to it. So this was about the artificial intelligence. Now coming to the machine learning part. So as I already said, machine learning is a subset or a current application of AI. It is based on the idea that we should be able to give machine the access to data and let them learn from themselves. It's a subset of artificial intelligence that deals with the extraction of pattern from data set. This means that the machine can not only find the rules for optimal behavior but also can adapt to the changes in the world. Many of the algorithms involved have been known for decades, centuries even. Thanks to the advances in the computer science and parallel computing, they can now scale up to massive data volumes. So this was about the machine learning part. Now coming over to deep learning. Deep learning is a subset of machine learning where similar machine learning algorithm are used to train deep neural network so as to achieve better accuracy in those cases where former was not performing up to the mark right I hope now you understood that machine learning AI and deep learning all three are different okay moving on ahead let's see in general how a machine learning work one of the approaches is where the machine learning algorithm is trained using a labeled or unlabelled training data set to produce a model. New input data is introduced to the machine learning algorithm and it make prediction based on the model. The prediction is evaluated for accuracy and if the accuracy is acceptable, the machine learning algorithm is deployed. Now if the accuracy is not acceptable, the machine learning algorithm is trained again and again with an augumented training data set. This was just an highle example as there are many more factor and other steps involved in it. Now let's move on and subcategorize the machine learning into three different types. the supervised learning, unsupervised learning and reinforcement learning and let's see what each of them are, how they work and how each of them is used in the field of banking, healthcare, retail and other domains. Don't worry, I'll make sure that I use enough examples and implementation of all three of them to give you a proper understanding of it. So starting with supervised learning, what is it? So let's see a mathematical definition of supervised learning. Supervised learning is where you have input variables X and an output variable Y and you use an algorithm to learn the mapping function from the input to the output that is Y= FX. The goal is to approximate the mapping function so well that whenever you have a new input data X you could predict the output variable that is Y for that data. Right? I think uh this was confusing for you. Let me simplify the definition of supervised learning. So we can rephrase the understanding of the mathematical definition as a machine learning method where each instances of a training data set is composed of different input attribute and an expected output. The input attributes of a training data set can be of any kind of data. It can be a pixel of image. It can be a value of a database row or it can even be audio frequency histogram. Right? For each input instance an expected output value is associated. The value can be discrete representing a category or can be a real or continuous value. In either case, the algorithm learns the input pattern that generate the expected output. Now once the algorithm is trained, it can be used to predict the correct output of a neverseen input. You can see an image on your screen. Right? In this image, you can see that we are feeding raw inputs as image of apple to the algorithm. As a part of the algorithm, we have a supervisor who keeps on correcting the machine or who keeps on training the machine. It keeps on telling him that yes, it is an apple and no, it is not an apple. Things like that. So this process keeps on repeating until we get a final train model. Once the model is ready, it can easily predict the correct output of a never-seen input. In this slide you can see that we are giving an image of a green apple to the machine and the machine can easily identify it as yes it is an apple and it is giving the correct result. Right? Let me make things more clearer to you. Let's discuss another example of it. So in this slide the image shows an example of a supervised learning process used to produce a model which is capable of recognizing the ducks in the image. The training data set is composed of label picture of ducts and non-ducts. The result of supervised learning process is a predictive model which is capable of associating a label duck or not duck to the new image presented to the model. Now once trained the resulting predictive model can be deployed to the production environment. You can say a mobile app for example. Once deployed it is ready to recognize the new pictures. Right now you might be wondering why this category of machine learning is named as supervised learning. Well, it is called as supervised learning because the process of an algorithm learning from the training data set can be thought of as a teacher supervising the learning process. We know the correct answers. The algorithm iteratively makes while predicting on the training data and is corrected by the teacher. The learning stops when the algorithm achieves an acceptable level of performance. Now let's move on and see some of the popular supervised learning algorithm. So we have linear regression, random forest and support vector machines. These are just for your information. We'll discuss about these algorithms in our next video. Now let's see some of the popular use cases of supervised learning. So we have Kotana. Kotana or any other speech automation in your mobile phone trains using your voice and once trained it start working based on the training. This is an application of supervised learning. Suppose you are telling okay Google call Sam or you say hey Siri call Sam you get an answer to it and the action is performed and automatically a call goes to Sam. So these are just an example of supervised learning. Next comes the weather app based on some of the prior knowledge like when it is sunny the temperature is higher when it is cloudy humidity is higher any kind of that they predict the parameters for a given time. So this is also an example of supervised learning as we are feeding the data to the machine and telling that whenever it is sunny the temperature should be higher whenever it is cloudy the humidity should be higher. So it's an example of supervised learning. Another example is biometric attendance where you train the machine and after couple of inputs of your biometric identity be it your thumb your iris or your earlobe or anything once trained the machine can validate your future input and can identify you. Next comes in the field of banking sector. In banking sector, supervised learning is used to predict the creditworthiness of a credit card holder by building a machine learning model to look for faulty attributes by providing it with a data on deloquent and non-eloquent customers. Next comes the healthcare sector. In the healthcare sector, it is used to predict the patients readmission rates by building a regression model by providing data on the patients treatment administration and readmissions to show variables that best correlate with readmission. Next comes the retail sector. In retail sector, it is used to analyze the product that a customer buy together. It does this by building a supervised model to identify frequent item sets and association rule from the transactional data. Now let's learn about the next category of machine learning. The unsupervised part. Mathematically unsupervised learning is where you only have input data X and no corresponding output variable. The goal for unsupervised learning is to model the underlining structure or distribution in the data in order to learn more about the data. So let me rephrase you this in simple terms. In unsupervised learning approach, the data instances of a training data set do not have an expected output associated to them. Instead, unsupervised learning algorithm detects pattern based on init characteristics of the input data. An example of machine learning task that applies unsupervised learning is clustering. In this task, similar data instances are grouped together in order to identify clusters of data. In this slide you can see that initially we have different varieties of fruits as input. Now these set of fruits as input X are given to the model. Now once the model is trained using unsupervised learning algorithm the model will create clusters on the basis of its training. It will group the similar fruits and make their cluster. Let me make things more clearer to you. Let's take another example of it. So in this slide the image below shows an example of unsupervised learning process. This algorithm processes an unlabelled training data set and based on the characteristics, it groups the picture into three different clusters of data. Despite the ability of grouping similar data into clusters, the algorithm is not capable to add labels to the group. The algorithm only knows which data instances are similar but it cannot identify the meaning of this group. So now you might be wondering why this category of machine learning is named as unsupervised learning. So these are called as unsupervised learning because unlike supervised learning ever there are no correct answer and there is no teacher algorithms are left on their own to discover and present the interesting structure in the data. Let's move on and see some of the popular unsupervised learning algorithm. So we have here K means a priori algorithm and hierarchal clustering. Again these are just for your information sake. We'll discuss about these algorithms in our next video. Now let's move on and see some of the examples of unsupervised learning. Suppose a friend invites you to his party and where you meet totally strangers. Now you'll classify them using unsupervised learning as you don't have any prior knowledge about them. And this classification can be done on the basis of gender, age group, dressing, educational qualification or whatever way you might like. Now why this learning is different from supervised learning? Since you didn't use any past or prior knowledge about the people, you kept on classifying them on the go. As they kept on coming, you kept on classifying them. Yeah, this category of people belong to this group. This category of people belong to that group and so on. Okay, let's see one more example. Let's suppose you have never seen a football match before and by chance you watch a video on the internet. Now you can easily classify the players on the basis of different criterion like player wearing the same kind of jersey are in one class player wearing different kind of jersey are in different class or you can classify them on the basis of their playing style like the guy is a attacker so he's in one class he's a defender he's in other class or you can classify them whatever way you observe the things. So this was also an example of unsupervised learning. Let's move on and see how unsupervised learning is used in the sectors of banking, healthcare and retail. So starting with banking sector. So in banking sector, it is used to segment customers by behavioral characteristic by surveying prospects and customers to develop multiple segments using clustering. In healthcare sector, it is used to categorize the MRA data by normal or abnormal images. It uses deep learning techniques to build a model that learns from different features of images to recognize a different pattern. Next is the retail sector. In retail sector, it is used to recommend the products to customer based on their past purchases. It does this by building a collaborative filtering model based on the past purchases by them. I assume you guys now have a proper idea of what unsupervised learning means. If you have any slightest doubt, don't hesitate and add your doubt to the comment section. So let's discuss the third and the last type of machine learning that is reinforcement learning. So what is reinforcement learning? Well, reinforcement learning is a type of machine learning algorithm which allows software agents and machine to automatically determine the ideal behavior within a specific context to maximize its performance. The reinforcement learning is about interaction between two elements the environment and the learning agent. The learning agent leverages two mechanism namely exploration and exploitation. When learning agent acts on trial and error basis, it is termed as exploration. And when it acts based on the knowledge gained from the environment, it is referred to as exploitation. Now this environment rewards the agent for correct actions which is reinforcement signal. Leveraging the rewards obtained, the agent improves its environment knowledge to select the next action. In this image, you can see that the machine is confused whether it is an apple or it's not an apple. Then the machine is trained using reinforcement learning. If it makes correct decision, it get rewards point for it. And in case of wrong, it gets a penalty for that. Once the training is done, now the machine can easily identify which one of them is an apple. Let's see an example. Here we can see that we have an agent who has to judge from the environment to find out which of the two is a duck. The first task he did is to observe the environment. Next he selects some action using some policy. It seems that the machine has made a wrong decision by choosing a bunny as a duck. So the machine will get penalty for it. For example, minus 50 point for a wrong answer. Right now the machine will update its policy and this will continue till the machine gets an optimal policy. From the next time machine will know that bunny is not a duck. Let's see some of the use cases of reinforcement learning. But before that let's see how Pavlo trained his dog using reinforcement learning or how he applied the reinforcement method to train his dog. Pavlo integrated learning in four stages. Initially Pavlo gave meat to his dog and in response to the meat the dog started salivating. Next what he did? He created a sound with the bell. For this the dog did not respond anything. In the third part he tried to condition the dog by using the bell and then giving him the food. Seeing the food the dog started salivating. Eventually a situation came when the dog started salivating just after hearing the bell. Even if the food was not given to him as the dog was reinforced that whenever the master will ring the bell, he will get the food. Now let's move on and see how reinforcement learning is applied in the field of banking, healthcare and retail sector. So starting with the banking sector in banking sector reinforcement learning is used to create a next best offer model for a call center by building a predictive model that learns over time as user accept or reject offer made by the sales staff. Fine. Now in healthcare sector it is used to allocate the scars medical resources to handle different type of ER cases by building a mark of decision process that learns treatment strategies for each type of ER case. Next and the last comes the retail sector. So let's see how reinforcement learning is applied to retail sector. In retail sector, it can be used to reduce excess stock with dynamic pricing by building a dynamic pricing model that adjusts the price based on customer response to the offers. [music] Machine learning is a branch of artificial intelligence that enable computers to learn patterns from data and make predictions or decisions without being explicitly programmed. So instead of following the rigid rules, ML models adapt and improve over time by analyzing vast amounts of data. From personalized recommendations on Netflix to fraud detection in banking, ML powers countless real world applications. So now that we have a basic understanding of machine learning, right? Now let's explore different types of ML models. So not all data is structured the same way and different problems require different approaches. So for example, predicting stock prices requires the models that learn from historical trends and then identifying objects in images needs model that recognize patterns in visual data. Next, the chat bots and voice assistants rely on the models train to understand and generate human language. So to tackle these challenges, as I discussed previously that ML is divided into different learning models such as supervised, unsupervised and reinforcement learning and each has its own strengths and it is used depending on the problem at hand. Since we know why different ML models are needed, let's see how they play a crucial role in generative AI. Well, generative AI is one of the most exciting applications of machine learning. And unlike traditional ML models that make predictions or classifications, generative models create entirely new content. And here's how ML enables AI to generate. So first here we have text. A language models like GPT generate humanlike text for chatbots, content writing, and coding. Next is the image. So AI powered tools like DALI can create realistic images from textual descriptions. Next is videos. So advanced ML models synthesize lielike video content, transforming media, marketing and even film making. So these advancements in generative AI are reshaping creativity and automation proving that machine learning is not just about making decision, it's about creating new possibilities. So now that we have seen how ML models enable AI to create new content. So now let us briefly understand the different types of machine learning models. So here the first type of machine learning model is supervised learning. Supervised learning trains a model using label data where each input has a corresponding correct output and this makes it ideal for task where historical data can be used to predict future outcomes. For example, let's say spam detection. Email services like Gmail uses supervised learning to classify emails as spam or not spam by learning from past labeled example. The next example is the price predictions. So real estate platforms use regression models to predict house prices based on the features like location, size and amenities. Now let us see some of the popular algorithms. So first let's discuss on decision trees. These models break down the data into a treel like structure where each note represent a decision based on a feature. So they are easy to interpret and work well for both classification. For example, deciding if an email is a spam or not and regression example predicting horse price. However, they can become overly complex. Next is the support vector machines. So SVMs are powerful for classification task as they find the optimal boundary also called a hyper plane and that best separates different classes in the data. They work well for highdimensional spaces and cases where the distinction between categories is clear such as handwriting, facial recognition or medical diagnosis. So now that we have seen how label data is used. So now let's explore how unsupervised learning finds pattern without labels. Well, unsupervised learning works with unlabelled data identifying hidden patterns and relationships without predefined categories. So here we have some of the popular algorithms. So first is the K means clustering. This algorithm partitions data into a predefined number of clusters by grouping similar data points based on their attributes. It works well for tasks like customer segmentation where businesses can group customer based on purchasing behavior. However, it assumes clusters are spherical and may struggle with irregular shaped data. Next, we have autoenccoders. So, these are specialized neural networks designed to learn efficient data representations by encoding and reconstructing input data. Let us see some of the examples. So, first example here we have is customer segmentation. When e-commerce platforms group customer based on their shopping behavior to offer personalized recommendations. The next example is market analysis. Businesses analyze purchasing trends to find association such as which products are frequently brought together. Now we have covered both labeled and unlabelled learning. So let's see how semi-supervised learning combines the best of both worlds. So semi-supervised learning bridges the gap between the supervised and unsupervised learning by using a small amount of labelled data along with large amount of unlabelled data. So for example, let's say AI assistant medical diagnosis. Labeled medical images such as X-rays with diagnosis are scarce, but large amounts of unlabelled images exist. Semi-supervised learning help AI learn patterns from both labeled and unlabelled data improving accuracy in disase detection. All right. Now let's explore the reinforcement learning where AI learns through trial and error. Well, reinforcement learning is inspired by the concept of learning through trial and error. So, models interact with an environment, receive rewards or penalties for actions, and refine their strengths over time. For example, let's say gaming. Mario AI developed using reinforcement learning, learns to navigate levels by optimizing actions through trial and error. The next example is robotics where robots learn to work, balance or perform tasks through reinforcement learning by maximizing positive outcomes. Also, reinforcement learning uses agents, actions and rewards to improve decision making it ideal for task requiring continuous learning and adaption. So now that we have covered all the types of machine learning models, so let's go over some of the key tips to help you choose the right one for your needs. So here are the tips. when it comes to supervised learning, classifying emails as spam or not and diagnosing disases from patient data. Next is the unsupervised learning. So unsupervised learning is best when you're grouping shoppers by behavior and detecting fraud in banking. Next we have semi-supervised learning and this is best when you're improving speech recognition with limited label data and identifying fake news. And finally the reinforcement learning. This will be best when you're training self-driving cars to navigate, optimizing AI in video games like Mario. So whether it's supervised, unsupervised, semi-supervised, or reinforcement learning, each model plays a crucial role in shaping AI's future. So as generative AI continues to evolve, this models are driving innovation in text, images, and video generation. So which machine learning model do you find the most fascinating? Let me know in the comments below. >> [music] >> Why mathematics in machine learning? Aspiring machine learning engineers often tend to ask me what is the use of mathematics machine learning when we have computers to do it all. Well, that is true. Our computers have become capable enough to do the math in split seconds where we would take minutes or even hours to perform the calculations. But in reality, it is not the ability [clears throat] to solve the math. Rather it is the eye of how the math needs to be applied. You need to analyze the data and infer information from it so that you can create a model that learns from the data. Math can help you in so many ways that it becomes mind-boggling that someone could hate this subject. Of course, doing math by hand is something I hate too. But knowing how I use math is enough to explain my love for math. So allow me to extend this love to you guys too because I won't be teaching you just the mathematics for machine learning but the various applications you can use it for in real life. So what math do we need to learn for machine learning? Here is a pie chart which comprises of all the needed math. Linear algebra covers a major part followed by the multivaried calculus. Statistics and probability also play a big role and you need to know the knowledge of algorithms and much more. This is the requirement that is needed to master machine learning. So now that we have developed this understanding, let's do some math. We shall kick off with linear algebra. Linear algebra is used most widely when it comes to machine learning. It covers so many aspects making it unavoidable if you want to learn mathematics for machine learning. Linear algebra helps you in optimizing data operations that can be performed on pixels such as sharing a rotation and much more. You can understand why linear algebra is such an important aspect when it comes to mathematics for machine learning. So let's move over to the first topic in linear algebra scalars. So what is a scalar? A scalar is basically a value. It represents something right? So scalas are just values that represent something thing. Suppose we had a laptop on sale and it is priced at 50,000 rupees right. So this 50,000 rupees is the scalar value of that laptop. What are the operations that can be performed on scalars? It is just basic arithmetic. So for example we have addition, subtraction, multiplication, division. All of those operations can be applied on scalars. Okay. For example, over here we are buying a laptop and the accessories. What is the total price? It'll be the addition of both the prices. So 50,000 for the laptop and 5,000 for the accessories brings it up to 55,000 rupees. What happens if you're buying a laptop at a 50% discount? So it is half the price, right? It is 50,000 divided by 2 that becomes 25,000 for the laptop. So this is just a brief introduction and all that is required from scalars. So once we are clear with this let's move over to vectors. So vectors can get a bit complicated as they are different for different backgrounds. Let me tell you how computer science people can interpret vectors as a list of numbers that represent something. Physicists consider vectors to be a scalar with a direction and it is independent of the plane. Mathematicians take vectors to be a combination of both and try to generalize it for everybody. All of these standpoints are absolutely correct and that's what makes it so confusing for anyone learning about linear algebra for mathematics for machine learning. In machine learning, we usually consider vectors in the standpoint of a computer scientist where the data is in the tabular form consisting of rows and columns. Right? And when our data is in the form of pixels or pictures, we consider them as vectors that are bound to the origin and transform them to matrices and perform operations that we shall discuss later. So now that you have a brief idea about vectors, let's jump over to the operations that you need to know when working with vectors. Operations on vectors can be applied only when you know what kind of data you're working with. Suppose you have pixel data and you want to apply rotations but end up doing something wholly different. Your model will not work because it is doing all the wrong operations here. It's important that you make sure that you know what you're working with only then you will be able to apply the required operations. So the first operation that we have here is vector addition. So let's understand what vector addition does. So for example vector addition is also called as dotproduct. Vector addition is something that is completely different from operations that we've been learning now for scalas. Okay, it's not simple arithmetic. It is actually the total work that is done by both the vectors in a quantified form. So for example, let me say that I want to walk forward by 50 m and that is one vector. Okay. Okay. So me walking forward for 50 m is one vector and from there I go right for 25 m right. So that is the second vector. So what is the work that is completely done by both these vectors is me moving forward and then moving right. So let me say for example v_sub_1 is what I walked forward. Okay. And then v_sub_2 is something that I moved right. So what is the addition of this? The addition is basically putting both the vectors point to point and then finding the displacement or the work that has been done. If you look at it over here, it is v_sub_1 plus v_sub_2's work that is in the quantified form of v_sub_1 + v_sub_2. It is the displacement. So for example, v_sub_1 is a distance and v_sub_2 is a distance. V_sub_1 + v_sub_2 is the displacement. So that is basically what is a dot product. I hope you've understood this. So let's move over to the next operation that is scalar multiplication. So what is scala multiplication? So whenever a vector is multiplied with a scalar value, it either grows or shrinks. What this means is that you have a particular value a scalar value which is either positive or it is negative and it may be greater than one or lesser than one. Whichever is lesser than one and it is negative, it'll always make it shrink or else it'll do the opposite. It'll make it grow. So let me just show you an example over here. here here. So let's say I have a vector called v_sub_1. Now if I'm trying to multiply this with a positive scalar value say k positive scalar value into v_sub_1 will make the vector grow. Whereas if I am trying to multiply this particular vector with a negative scalar value say minus k it will be shrinking down down. So it is minus k into v1 gives me a shrink vector. So as you can see this was my normal vector and if I multiplied it with a constant k which was positive it grew and if it was negative it shrink down. So that is basically what is scalar multiplication. So the next vector operation is a projection. So what does projection help us with? So for example, let's say I have two vectors, okay, v_sub_1 and v_sub_2. Now I do not know much about v_sub_1 and I just know more about v_sub_2. So if I can try to find a way in which I can project the vector v_sub_1 onto v_sub_2, I'll be able to obtain information about v_sub_1. So let me just show you. So for example I have a vector v_sub_1 and I had another vector v_sub_2. So I know all about v_sub_2 but I do not know about v_sub_1 vector. So what happens over here is if I'm able to project the projection of vector v_sub_1 onto v_sub_2 I will be able to analyze and know the unknown features that vector v_sub1 has. Okay. Actually, if you go with this into deep learning, right, you can be able to find unknown features of the vector which can help you modify your one image into so many images that you can basically simplify and modify that image into something that it is not. Okay, that comes under deep learning but we are not going to cover that. But this is a very important concept that you need to understand. It is basically like it's said over here. Projection is the shadow of a vector that it places on the other vector. So whatever information that v_sub_1 vector has, I'll be able to somehow extract it from the vector v_sub_2 because the projection falls onto v_sub_2. That basically brings us to the end of all the vector operations that you need to remember for machine learning. Let's move over to matrices. So what is a matrix? A matrix is the composition or it is the mixture of numbers, symbols, expressions which are in a rectangular array. It can be rectangular, it can be square, it depends on the order. So what do we use matrices for? We use matrices to convert our equations into the form of arrays. For example, if you've got an equation, you cannot simply put that into your computer saying that okay, solve this and give it to me. You need to convert it into a list or an array so that you'll be able to perform your operations on it. Right? That is the reason matrices are so much important to us and that is the reason it is much more easier for us so that we can convert our equations into uh lists and arrays and then perform our operations on them. So suppose for example you have two equations over here. So how do you convert these two equations into matrices. So what does a equation tell you? If you have 2x + 2 y is equal to 10. What this basically is trying to convey the information to you is that you have two constants x and y. In these constants if you keep giving different numbers you'll be able to find a different value for it. Let's say for example the scala value is 10 and you have 2x + 2 y which is basically a vector. I need to find the points of x and y. Find the points of x and y meaning that I'm trying to find the direction of the vector and then if I'm able to substitute values and then find out how 2x + 2 y is equal to 10. I'm finding all the information I need from that vector so that I can basically find out what all the other information I need from it. That is how functions are very important. You need to understand what a function is trying to convey to you. Let's say for example you have the equation of a straight line. So what does a straight line be? It is y is equal to mx + c. What does this mean? It means that the y-coordinate is equal to some value m into x plus a constant. So I'm able to plot this. I'll be getting the y-coordinate, the x coordinate and I'll be able to get a straight line. So whatever numbers I put into these, I will always be getting a straight line. So that is the reason it is called the equation of a straight line. It is always going to be constant. So you have to understand what a function is trying to convey to you. Once we are done with that, let me just tell you how you convert equations into matrices. It's really simple. Take out all the numbers. So you have 2x + 2 y = 10, right? So 2x and 2 y has two numbers, two. So those two become one row. 4 and 1 in the second equation become one row. X and Y becomes one column and 10 and 18. So let me just show it to you. So as you can see we have a matrix 22 41 then we have x and y is equal to 10 and 18. If you multiply it accordingly you'll be getting back the same equation that we had earlier. This is how matrices are used in linear algebra. So once you know how the equations are converted into matrices let's move over to the matrix operations. So what is the first operation? Simple addition. What does addition help you with? It is just basically adding all the directions of two vectors. Why is it two vectors? Because I'm converting vectors into matrices, right? You are simply just going to add the corresponding elements of both the matrices. Simply add the corresponding elements of both the matrices. And you have to remember that if you are adding two matrices, it has to be of the same order. What do I mean by order? It is basically the number of rows into the number of columns. So for example, if I have the first matrix that is 22 2 4 and 1. I have two rows and I have two columns. So that becomes a 2 +2 matrix. That is the order of the matrix. The next one also 2 3 1 4. It has two rows and two columns. That makes it an order of 2 +2. So if I had three rows and I had two columns, it would be 3 into 2. So I hope you have understood what a order is. Let's say I had these two matrices and I want to add them. So what I do? It is 2 + 2. So let's say I have two over here and I have two over here. So what is 2 + 2? It becomes 4. What is 2 + 3? It becomes 5. What is 4 + 1? it becomes five. What is 1 + 4? It becomes five. So, it is adding the corresponding elements of the matrix. So, I hope you've understood that. So, let's move over to the next operation. Matrix subtraction. It's the same thing as how you did it for addition. You just subtract the corresponding elements. If you had 2 - 2, it becomes 0. 2 - 3 becomes -1. 4 - 1 becomes 3. 1 - 4 becomes - 3. Simple. You can understand this very easily. Moving ahead from matrix subtraction is matrix multiplication. What do you do with matrix multiplication? You are basically multiplying the rows with the columns. The matrix of row one with the columns of matrix 2. What happens? You have to remember that the number of rows in matrix one has to be equal to the number of columns in matrix 2. Only then will you be able to perform the matrix multiplication. So for example, if I had a 2 +2 matrix, it would be a11 into b11, a12 into b21, a11 into b12 plus the a12 into b22 accordingly. So let me show you an example for matrix multiplication so that you can understand how it works. Suppose I have a 2 +2 matrix that I've already been using for matrix addition and subtraction. Now how am I going to perform the matrix multiplication is basically I'm going to you know multiply the first row into both the columns of the matrix 2. So I have 2 into 2 + 2 into 1. Then I have 2 into 3 + 2 into 4. The same thing goes for the second row also. So what do I get? I get 4 + 2 6 + 8 8 + 1 and 12 + 4. That accordingly gives me 6 14 9 and 16. So this is the matrix multiplication. It's really simple to understand. So if you have any doubts, leave them in the comment section. We'll get back to you as soon as possible. So once we are done with matrix multiplication, let's move over to the transpose. So the transpose is a really simple operation. All you do is you convert the rows into columns. That's it. But why is it so important? Transpose is really important when you want to change the dimensionality of your data. Suppose all your data is in a row. you can reiterate through there or all your data is in a column you can do it accordingly. So it is really important when you work with transpose because it helps you to change the dimensionality it helps you flip the dimensions. So for example if you're working with pixels right pictures if you change the rows or the columns of your pictures data you are basically changing the picture and then you can you know analyze it more get more information from it. Transpose plays a very important role. You need to understand that. So for example, I have 2 4 and 1. What happens is the first column becomes the first row and the second row becomes the second column. So as you can see here it is 2 2 4 and 1. And that is all transpose is. So let's move over to the next operation. We have determinant of a matrix. By now all we have been doing is having matrices being added, subtracted. So what is all of this is it is basically all the vectors being added, subtracted, multiplied, you know, then flipped with their dimensions. You will understand this when you do all of this practically because all of this is something that we do not do it in our daily lives. But when you're learning with machine learning, when you're performing machine learning, all of these operations come into picture. So all that you've learned by now is basically adding values of vectors, subtracting vectors, multiplying two vectors, then transpose that is the flipping of vectors. And now you're going to learn about determinant. What is a determinant? All the matrices that we had till now, they are basically directions. They are basically directions and values of all the vectors. Now all these vectors are definitely going to have a scalar value in them. so that you can understand the weight. You can understand the depth of that particular matrix. What is the determinant helping you with? With the determinant helps you with understanding the weight or the you know sensitivity that it can provide on the data set. That is the reason determinant is really important. It is the scalar value of the matrix and it can help you give the igen values of the matrix. What do I mean by values? I'll teach that to you in the next part because we are going to understand in depth what are igen values and igon vectors. That is the reason determinants are so important. So let's say for example I had this particular matrix a b c d f g hi. It would be a into ef hi and then it would be minus b into df gi plus c into d e gh. So what happens now is I'm going to get this particular equation. So it's a EI plus BFG plus CD H minus A FH minus BDI minus CG. This is basically what is going to give me the scalar value of the matrix. So I hope you've understood the importance and how determinants are important in machine learning. So next we will learn about the inverse of a matrix. So how do I explain inverse to you? It's a very simple example if you understand that. Suppose I am walking on a road and I walked straight for 50 m. But then I remember that I had to get back something from the place I started. So I walked back 50 m. What is the distance that I traveled? The distance that I traveled was 100 m. Why? Because I went 50 m forward and 50 m backward. But what is the work that I have done? it is zero. Why is that? It is because I'm at the same place that I started from. That is not the work done. If I move from one place to another place, that is the work done. That is some displacement that my body has achieved. But I have not achieved that over here. Why? It's because I have gone straight and come back straight for 50 m making my work done zero. So just the same way inverse of a matrix works. Suppose we have a vector that moves in the forward direction. you will have the inverse of that particular vector that comes in the negative direction and it makes all the work done zero. Sometimes there is no inverse of a matrix that exists. That's because the vector does not have all the information that is required to obtain its inverse. So I hope you have understood what is a inverse. Let's see how do you find an inverse of it. Okay, for a 2 +2 matrix this is how you're going to find it. it is finding the determinant into the transpose or you know finding the inverse of the matrix. So it is a and d that is going to be you know switched over and minus b and minus c. This gives you the inverse of the matrix. So for orders three and above what you do do you find the determinant of a and then you accordingly find all the different determinants inside of it. So that is basically how you find the inverse of a matrix. Let's move over to how a vector can be used as a matrix. Okay. So by now that I've been telling that vectors can be easily translated into matrices and I've already shown it to you. And why is it so important? It's because they help you apply operations on the data very easily. And then you have certain well-known operations such as scaling, rotation, sharing and much more. All of this come under computer graphics. Okay. making these operations on your image or your vectors becomes really easy when you're working with matrices. So that's the reason matrices are so important. So for example, right now I've shown you that if there was an equation v1 as 3x + 4, it would be 3 and 4 and then you had x and y. Then you would have x + 2 y which would become 1 and 2 and then x and y. That is how vector as a matrix works. What are some of the well-known operations? Right? I'm assuming that there is going to be a 2 +2 matrix. Whenever you're scaling, it is basically increasing the size. So, how do you increase the size? It is sx and sy which are the scaling factors which you perform on your x and y coordinates. Then you have sharing which is basically moving or reshaping your particular object that you're working with. So, it can be m which is the sharing factor. And then you have the rotation. So how do you rotate your particular object in which direction? So all of that can be done using these particular matrices. So let's move over and understand how matrices can help you solve equations and you know obtain solutions much more easily. So that is basically vector as a matrix. We have two methods over here. They are the echelon method and the inverse method. For our tutorial I've been taking the row echelon method because it's much more comfortable for me. If you are much more comfortable with column echelon method, you can go ahead with that. But because I am comfortable with row echelon methods, I've used row echelon method. And next we have the inverse method. So we are basically going to solve the equations. We are going to find the coordinates at which our points give us that particular value. So let's move over with the first method which is the row echelon method. And I have some equations over here which go ahead like 2x + y - z = 2 x + 3 y + 2 z = 1 x + y + z = 2. So I'm going to convert all of this into a particular matrix. So let me show you how the matrix looks. It is 2 1 - 2 and 2 1 3 2 1 and 11 1 1. So all the information about the equations have been put into the matrix form and the answers that we're going to get are x= 2, y is equal to minus1 and z is equal to 1. So this is the reason I'm going to get all these particular values that is 2 1 and 2 which I'm getting from the equations. Whenever I put the x, y and z values into them I'm going to you know get those particular coordinates. Now let me just tell you why we are solving equations. Okay. So if I am telling that there is this particular vector that goes like this or comes in this direction or something like that. I want to find the x y and z coordinates so that I can obtain the information visualize it and then learn more about that particular vector. Now say for example this is just 2x + y - z equal to 2. Let's say for example if what if it was a two boxes plus one candle minus one chocolate is equal to giving me a profit of 2 rupees. Okay so as you can see these are just simple equations and these are the coordinates that we get x= 2 y is equal to minus1 and z is equal to 1. But what is the importance of this okay let me just give you a simple example so that you can understand what we are actually trying to find out over here. Okay, suppose I have a factory and I want to get a profit of 2 rupees and I have boxes, I have candles and I have chocolates. So if I take the first equation, I'm saying that if I have two boxes, one candle minus the chocolate, it is going to give me 2 rupees profit. So what is X, Y, and Z exactly? X, Y, and Z are the investment costs. How much do I need to invest into them so that I can get back what I really required? So for boxes I need to invest 2 rupees. For uh chocolates I need to invest nothing. For candles I need to invest minus one or something like that. Okay. If I invest so much I'm going to get 2 profit. So this is like a real life example which is being converted into some equation and t