Great.
With 22+ hours of content and 200+ video lessons, this course covers everything in Linear Algebra, from start till the end.
Every concept is explained in simple language, and Quizzes and Assignments (with solutions. ) help you test your concepts as you proceed.
Whether you're a student, or a professional or a Math enthusiast, this course walks you through the core concepts of Linear Algebra in an easy and fun way.
· Operations on a single matrix, e.g. scalar multiplication, transpose, determinant, adjoint etc.
Read more
Great.
With 22+ hours of content and 200+ video lessons, this course covers everything in Linear Algebra, from start till the end.
Every concept is explained in simple language, and Quizzes and Assignments (with solutions. ) help you test your concepts as you proceed.
Whether you're a student, or a professional or a Math enthusiast, this course walks you through the core concepts of Linear Algebra in an easy and fun way.
· Operations on a single matrix, e.g. scalar multiplication, transpose, determinant, adjoint etc.
Great.
With 22+ hours of content and 200+ video lessons, this course covers everything in Linear Algebra, from start till the end.
Every concept is explained in simple language, and Quizzes and Assignments (with solutions. ) help you test your concepts as you proceed.
Whether you're a student, or a professional or a Math enthusiast, this course walks you through the core concepts of Linear Algebra in an easy and fun way.
· Operations on a single matrix, e.g. scalar multiplication, transpose, determinant, adjoint etc.
· Operations on two matrices, including addition, subtraction and multiplication
· Performing elementary row operations and finding Echelon Forms (REF & RREF)
· Inverses, including invertible and singular matrices, and the Cofactor method
· Solving systems of equations using matrices & inverse matrices, including Cramer’s rule to solve AX = B
· Performing Gauss-Jordan elimination
· Properties of determinants and how to utilize them to gain insights
· Matrices as vectors, including vector addition and subtraction, Head-to-Tail rule, components, magnitude and midpoint of a vector
· Linear combinations of vectors and span
· Vector spaces, including dimensions, Euclidean spaces, closure properties and axioms
· Subspace and Null-space of a matrix, matrix-vector products
· Spanning set for a vector space and linear dependence
· Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
· Eigenvalues and Eigenvectors, including how to find Eigenvalues and the corresponding Eigenvectors
· Basic algebra concepts (as a BONUS)
· And so much more….. Everything is taught from scratch, and no prior knowledge is assumed.Solved Examples: Every topic is explained with the help of solved examples, from start to end. This problem-based approach is great, especially for beginners who want to practice their Math concepts while learning.Quizzes: When you think you have understood a concept well, test it by taking the relevant quiz. If you pass, awesome. Otherwise review the suggested lessons and retake the quiz, or ask for help in the Q/A section.Assignments: Multiple assignments offer you a chance for additional practice by solving sets of relevant and insightful problems (with solutions provided)By the end of this course, you'll feel confident and comfortable with all the Linear Algebra topics discussed in this course.
· Linear Algebra is a prerequisite for many lucrative careers, including Data Science, Artificial Intelligence, Machine Learning, Financial Math, Data Engineering etc.
· Being proficient in Linear Algebra will open doors for you to many high-in-demand careers
I took this Linear Algebra class at University of Illinois at Urbana Champaign, one of the Top-5 Engineering Schools in the country, and I have tried to follow the same standards while designing this course.
I have taught various Math and Engineering courses for more than 10 years at schools across US, Asia and Africa. I strongly believe that I have the ability to breakdown complex concepts into easily understandable chunks of information for you.
I provide premium support for all my students - so if you ever get stuck or have a question, just post it to the course dashboard and I'll be there to help you out in a prompt and friendly way.
My goal is to make this the best Linear Algebra and Math course online, and I'll do anything possible to help you learn. I needed to get a better understanding and a good base of Linear Algebra for Data Science and Machine Learning and Kashif absolutely delivered. This is definitely a Zero to Hero course on Linear Algebra in my opinion, and would highly recommend this to anyone who is on the same path as I am. Nothing but appreciation for this author.” – I. Valderrama“Wish I had found this earlier” - Dan“Great explanations. Solid teaching” - J. P. Baugh“Excellent course. The course material is really good, explanation is really clear and every new concept is provided with examples that make the experience even better. The instructor always takes the time to answer questions poster in Q&A. New material is constantly added to course. Thank you. ” – K. GeageaYOU'
Feel free to check out the course outline below or watch the free preview lessons. Or go ahead and enroll now.
I can’t wait for you to get started with Linear Algebra.
Cheers,Kashif
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What's inside
Learning objectives
- Fundamentals of linear algebra and how to ace your linear algebra exam
- Basics of matrices (notation, dimensions, types, addressing the entries etc.)
- Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
- Operations on two matrices, including addition, subtraction and multiplication of matrices
- Performing elementary row operations and finding echelon forms (ref & rref)
- Inverses, including invertible and singular matrices, and the cofactor method
- Solving systems of linear equations using matrices and inverse matrices, including cramer’s rule to solve ax = b
- Properties of determinants, and how to perform gauss-jordan elimination
- Matrices as vectors, including vector addition and subtraction, head-to-tail rule, components, magnitude and midpoint of a vector
- Vector spaces, including dimensions, euclidean spaces, closure properties and axioms
- Linear combinations and span, spanning set for a vector space and linear dependence
- Subspace and null-space of a matrix, matrix-vector products
- Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
- Eigenvalues and eigenvectors, including how to find eigenvalues and the corresponding eigenvectors
- Basic algebra concepts ( as a bonus)
- And so much more…..
- Show more
- Show less
- Fundamentals of linear algebra and how to ace your linear algebra exam
- Basics of matrices (notation, dimensions, types, addressing the entries etc.)
- Operations on a single matrix, e.g. scalar multiplication, transpose, determinant & adjoint
- Operations on two matrices, including addition, subtraction and multiplication of matrices
- Performing elementary row operations and finding echelon forms (ref & rref)
- Inverses, including invertible and singular matrices, and the cofactor method
- Solving systems of linear equations using matrices and inverse matrices, including cramer’s rule to solve ax = b
- Properties of determinants, and how to perform gauss-jordan elimination
- Matrices as vectors, including vector addition and subtraction, head-to-tail rule, components, magnitude and midpoint of a vector
- Vector spaces, including dimensions, euclidean spaces, closure properties and axioms
- Linear combinations and span, spanning set for a vector space and linear dependence
- Subspace and null-space of a matrix, matrix-vector products
- Basis and standard basis, and checking if a set of given vectors forms the basis for a vector space
- Eigenvalues and eigenvectors, including how to find eigenvalues and the corresponding eigenvectors
- Basic algebra concepts ( as a bonus)
- And so much more…..
- Show more
- Show less
Syllabus
Welcome and Introduction
This video is to officially welcome you to the Linear Algebra course. I give an overview of the topics covered, and the strategies to get the most out of this course!
Read more
Syllabus
This video is to officially welcome you to the Linear Algebra course. I give an overview of the topics covered, and the strategies to get the most out of this course!
In this quiz, we practice how to specify the Dimensions of a Matrix.
In this quiz, we practice how to address or refer to the elements of a matrix.
In this quiz, we practice how to solve systems of 2 linear equations in 2 unknowns, without using matrices.
In this quiz, we practice how to solve systems of 3 linear equations in 3 unknowns, without using matrices.
https://matrix.reshish.com/
In this lesson of the Linear Algebra course, we look at how to represent a system of 2 linear equations in the 2x2 Matrix form.
In this lesson of the Linear Algebra course, we look into how to write a system of 3 linear equations in the form of a 3x3 matrix and solve it.
In this lesson of the Linear Algebra course, we see how to perform different types of row operations on a matrix to convert it into Row Echelon Form (REF).
In this lesson of the Linear Algebra course, we learn what the Row Echelon Form (REF) of a matrix is, and how to compute it.
In this lesson of the Linear Algebra course, we learn what the Reduced Row Echelon Form (RREF) of a matrix is, and how to obtain it.
In this lesson of the Linear Algebra course, we learn how to perform addition and subtraction of matrices.
In this lesson of the Linear Algebra course, we learn how a scalar can be multiplied to a matrix, and what are the rules for that.
In this lesson of the Linear Algebra course, multiplication of two matrices with each other is explained, using examples.
In this lesson of the Linear Algebra course, we learn how to get transpose of a given matrix.
In this lesson of the Linear Algebra course, we learn how to compute determinant of a 2x2 matrix.
In this lesson of the Linear Algebra course, we learn how to compute determinant of a 3x3 matrix.
In this lesson of the Linear Algebra course, I discuss some shortcuts that we can possibly use in certain cases to find determinants quickly and easily.
In this lesson of the Linear Algebra course, we learn why inverse can be calculated only for square matrices, and why inverse doesn't exist for non-square matrices.
In this lesson of the Linear Algebra course, we learn what the term Singular Matrix means, and how is it related to the inverse of a matrix.
In this lesson of the Linear Algebra course, we see why finding inverse of the coefficient matrix is important and helpful for solving a linear system.
In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 1.
In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 2.
In this lesson of the Linear Algebra course, we look at the property of the determinants that deals with the matrix row operation 3.
In this lesson of the Linear Algebra course, we summarize the properties of the determinants that deal with the matrix row operations.
In this lesson of the Linear Algebra course, we apply our knowledge of the properties of determinants.
In this lesson of the Linear Algebra course, we look at one more property of the matrix determinants that is very helpful..
In this lesson of the Linear Algebra course, you are introduced to the Vector Spaces.
In this lesson of the Linear Algebra course, we discuss what Euclidean vector spaces are.
In this lesson of the Linear Algebra course, Euclidean vector spaces are discussed in further detail, in continuation of the previous lesson.
In this lesson of the Linear Algebra course, further explanation is provided on the topic of Euclidean vector spaces.
In this lesson of the Linear Algebra course, we look into what Closure Properties are, and how these are used as a criteria to check for vector spaces.
In this lesson of the Linear Algebra course, the ten fundamental axioms for vector spaces are listed and explained.
In this lesson of the Linear Algebra course, examples of closure properties are discussed.
In this lesson of the Linear Algebra course, we discuss an example of vector spaces to clarify the concept.
In this lesson of the Linear Algebra course, one more example of vector spaces is discussed.
In this lesson of the Linear Algebra course, you are introduced to the topic of Subspaces.
In this lesson of the Linear Algebra course, subspaces are explained with the help of example 1.
In this lesson of the Linear Algebra course, subspaces are further explained with the help of example 2.
In this lesson of the Linear Algebra course, subspaces are further explained with the help of example 3.
In this lesson of the Linear Algebra course, the topic of Nullspace of a matrix is discussed and explained..
In this lesson of the Linear Algebra course, nullspaces are further explained with the help of an example.
In this lesson of the Linear Algebra course, we discuss what does the span of a set of given vectors means, and how to compute that.
In this lesson of the Linear Algebra course, we further discuss the span of a set of given vectors through an example.
In this lesson of the Linear Algebra course, we discuss the notion of spanning set for a vector space using a few examples.
In this lesson of the Linear Algebra course, spanning sets are further explained with the help of example 3.
In this lesson of the Linear Algebra course, spanning sets are further explained with the help of example 4.
In this lesson of the Linear Algebra course, we look into the notion of linear dependence and linear independence.
In this lesson of the Linear Algebra course, formal definition of linear dependence is presented and discussed.
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Reviews summary
Intuitive linear algebra
Instructor answers questions in a clear way.
Explanations were clear.
Activities
Attend a Math Club Meeting
Show steps
This course is a great opportunity to meet other students who are interested in math, including linear algebra.
Browse courses on
Linear Algebra
Show steps
-
Find a local math club and attend a meeting.
-
Introduce yourself to other students and ask them about their interests.
-
Talk to the club advisor about your goals for learning linear algebra.
Review Linear Algebra and Its Applications
Show steps
To be successful in this course, it is important for you to have a strong basis in the theory of Linear Algebra, which this textbook provides.
View
Linear Algebra for Everyone
on Amazon
Show steps
-
Start by reading the introduction to Linear Algebra and its applications.
-
Next, read the chapters on matrices, vectors, and systems of linear equations.
-
Finally, read the chapters on eigenvalues and eigenvectors, and on applications of linear algebra.
Practice Solving Systems of Linear Equations
Show steps
To be successful in this course, it is important for you to be able to solve systems of linear equations. This activity will give you the practice you need.
Show steps
-
Start by solving some simple systems of linear equations.
-
Then, try to solve some more challenging systems.
-
Finally, try to solve some systems of linear equations that involve complex numbers.
Three other activities
Expand to see all activities and additional details
Show all six activities
Form a Study Group
Show steps
This course is challenging, but it is more fun, and more achievable, when you study with friends.
Browse courses on
Linear Algebra
Show steps
-
Find a group of students who are also taking this course.
-
Meet regularly to discuss the course material.
-
Work together on problem sets and projects.
Participate in a Math Competition
Show steps
This competition is a great way to test your skills in linear algebra and to meet other students with similar interests.
Browse courses on
Linear Algebra
Show steps
-
Find a math competition that you are interested in participating in.
-
Register for the competition and start preparing.
-
Take the competition and see how you do.
Develop a Linear Algebra Project
Show steps
This project will allow you to apply the concepts of linear algebra to a real-world problem.
Show steps
-
Start by choosing a topic for your project.
-
Next, develop a plan for your project and outline the steps that you will take to complete it.
-
Finally, write a report on your project and present it to the class.
Attend a Math Club Meeting
Show steps
This course is a great opportunity to meet other students who are interested in math, including linear algebra.
Browse courses on
Linear Algebra
Show steps
- Find a local math club and attend a meeting.
- Introduce yourself to other students and ask them about their interests.
- Talk to the club advisor about your goals for learning linear algebra.
Review Linear Algebra and Its Applications
Show steps
To be successful in this course, it is important for you to have a strong basis in the theory of Linear Algebra, which this textbook provides.
View
Linear Algebra for Everyone
on Amazon
Show steps
- Start by reading the introduction to Linear Algebra and its applications.
- Next, read the chapters on matrices, vectors, and systems of linear equations.
- Finally, read the chapters on eigenvalues and eigenvectors, and on applications of linear algebra.
Practice Solving Systems of Linear Equations
Show steps
To be successful in this course, it is important for you to be able to solve systems of linear equations. This activity will give you the practice you need.
Show steps
- Start by solving some simple systems of linear equations.
- Then, try to solve some more challenging systems.
- Finally, try to solve some systems of linear equations that involve complex numbers.
Form a Study Group
Show steps
This course is challenging, but it is more fun, and more achievable, when you study with friends.
Browse courses on
Linear Algebra
Show steps
- Find a group of students who are also taking this course.
- Meet regularly to discuss the course material.
- Work together on problem sets and projects.
Participate in a Math Competition
Show steps
This competition is a great way to test your skills in linear algebra and to meet other students with similar interests.
Browse courses on
Linear Algebra
Show steps
- Find a math competition that you are interested in participating in.
- Register for the competition and start preparing.
- Take the competition and see how you do.
Develop a Linear Algebra Project
Show steps
This project will allow you to apply the concepts of linear algebra to a real-world problem.
Show steps
- Start by choosing a topic for your project.
- Next, develop a plan for your project and outline the steps that you will take to complete it.
- Finally, write a report on your project and present it to the class.
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