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The prerequisite to the course Linear Algebra for Beginners: Open Doors to Great Careers 2.
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Would you like to learn a mathematics subject that is crucial for many high-demand lucrative career fields such as:
If you're looking to gain a solid foundation in Linear Algebra, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on linear algebra or a complete beginner who needs to learn Linear Algebra for the first time, this online course is for you.
Why you should take this online course: You need to refresh your knowledge of linear algebra for your career to earn a higher salary. You need to learn linear algebra because it is a required mathematical subject for your chosen career field such as computer science or electrical engineering. You intend to pursue a masters degree or PhD, and linear algebra is a required or recommended subject.
Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.
In this course, I cover the core concepts such as:
After taking this course, you will feel CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.
Practice problems are provided for you, and detailed solutions are also provided to check your understanding.
30 day full refund if not satisfied.
Grab a cup of coffee and start listening to the first lecture. I, and your peers, are here to help. We're waiting for your insights and questions! Enroll now!
In this lecture, we discuss Gaussian Elimination and examples of solving a system of linear equations.
Students will learn about the three moves in Gaussian elimination.
In this lecture, the row echelon form is introduced and many examples of Gaussian elimination are worked out.
Students will learn how to apply Gaussian elimination to solve systems of linear equations. Students will also see the three different cases in regard to solutions to systems of equations.
Practice problems for Gaussian elimination
Solutions to Problem set Gaussian elimination
Detailed solutions are provided if needed.
The augmented matrix is introduced and the elementary row operations are defined.
Students will learn how to apply elementary row operations to an augmented matrix.
An additional example of applying row operations is provided.
Practice problems for Elementary Row Operations
Solutions to Problem set Elementary Row Operations
Detailed solutions to the problem set Elementary Row Operations are provided, if needed.
The vector operations of addition, scalar multiplication, and matrix multiplication are introduced and the definition of linear combination is provided.
Students will learn how to add two vectors, multiply a vector by a scalar, and multiply a vector by a matrix. The student will understand what linear combinations are and what weights are.
Practice problems for Vector Operations and Linear Combinations
Solutions to Problem set Vector Operations and Linear Combinations
In this lecture, the notion of span is introduced and it is shown how a system of equations can be rewritten as a matrix equation.
The notion of linear independence is introduced.
An example of determining linear independence is provided.
Students will learn how to determine when a set of vectors is linearly independent.
A second example of determining linear independence is provided.
Students will learn how to determine when a set of vectors is linearly independent.
Practice problems for Linear Independence
Solutions to Problem set Linear Independence
Detailed solutions to problem set Linear Independence are provided, if needed.
The matrix operations of addition and scalar multiplication are introduced.
Students will learn how to add two matrices and how to multiply a matrix by a scalar.
The matrix operation of multiplication is introduced.
Students will learn how to multiply two matrices.
Practice problems for Matrix Operations
Solutions to Problem set Matrix Operations
The properties of additive commutativity and associativity are introduced. The distributivity properties are also introduced.
Students will learn how to apply the additive commutativity, additive associativity, and distributivity properties.
The properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity are introduced.
Students will learn how to apply properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity.
Practice problems for Properties of Matrix Operations
Solutions to Problem Set Properties of Matrix Operations
Detailed solutions to problem set Properties of Matrix Operations is provided, if needed.
The definition of transpose of a matrix is provided, and properties of the transpose are introduced.
Students will learn how to find the transpose of a matrix and how to apply properties of transposes.
Practice problems for Transpose of a Matrix.
Solutions to Problem Set Transpose of a Matrix
Detailed solutions to Problem Set Transpose of a Matrix are provided, if needed.
The definition of inverse matrix is introduced and the formula for the inverse of a 2 by 2 matrix is given.
Students will learn what an inverse matrix is.
The process of Gauss-Jordan Elimination is explained.
Students will learn how to find the inverse of a matrix using Gauss-Jordan Elimination.
An additional example of Gauss-Jordan Elimination is provided.
Practice problems for Inverse of a Matrix
Solutions to Problem Set Inverse of a Matrix
Detailed solutions to Problem set Inverse of a Matrix are provided, if needed.
The formula for the determinant of a 2 by 2 matrix is introduced.
Students will learn how to find the determinant of a 2 by 2 matrix.
The process of Cofactor Expansion is explained.
Students will learn how to apply cofactor expansion to find the determinant of a 3 by 3 matrix.
Additional examples of cofactor expansion are provided.
Practice problems for Determinants
Solutions to Problem Set Determinants
Detailed solutions to Problem set Determinants are provided, if needed.
The determinant of a product of two matrices and the determinant of a scalar multiple of a matrix are discussed.
Students will be able to find the determinant of a product of matrices and the determinant of a scalar multiple of a matrix.
The relationship between determinants and invertibility is explained.
Students will be able to determine when a matrix is invertible by examining the determinant.
The determinant of the transpose of a matrix is discussed.
Students will learn how to find the determinant of the transpose of a matrix.
Practice problems for Properties of Determinants
Solutions to Problem set Properties of Determinants
Detailed solutions to Problem set Properties of Determinants are provided, if needed.
The definition of vector space is explained.
Students will learn what a vector space is.
A proof is given to show that R2 is a vector space.
Students will learn how to prove a set is a vector space.
The proof of the claim that R2 is a vector space is continued.
An additional example of a vector space is provided.
The proof of the first five properties of a vector space applied to P2 is continued.
Practice problems for Vector Spaces.
Solutions to Problem Set Vector Spaces
Examples of sets that are not vector spaces are discussed.
Students will learn how to detect when a set is a not a vector space.
Practice problems for Sets that are not vector spaces.
Solutions to Problem set Sets that are not vector spaces.
The definition of a subspace is provided, and the three subspace properties are outlined. An example of a proof showing that a subset of R2 is a subspace is demonstrated.
Students will learn how to show that a subset of a vector space is a subspace.
The definition of a trivial subspace and of a nontrivial subspace are provided.
An example of a subspace of M(2,2), the set of all 2 by 2 matrices, is provided.
Practice problems for Subspaces
Solutions to Problem Set Subspaces
An example of a subset of R2 that is not a subspace of R2 is discussed.
Students will learn how to show that a subset of a vector space is not a subspace of that vector space.
An additional example of a subset that is not a subspace is discussed.
Practice problems for Subsets that are not subspaces.
Solutions to Problem Set Subsets that are not subspaces.
Hi there! My name is Richard Han. I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International. My expertise includes calculus and linear algebra. I am an instructor on Udemy for the courses Philosophy of Language: Solidify Critical Thinking Skills and Linear Algebra for Beginners: Open Doors to Great Careers.