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Linear Algebra for Beginners: Open Doors to Great Careers

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Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more!

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- 7 hours on-demand video
- 46 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

- Refresh your math knowledge.
- Gain a firm foundation in Linear Algebra for furthering your career.
- Learn one of the mathematical subjects crucial for Computer Science.
- Learn one of the mathematical subjects crucial for engineering, computer science, physics, economics, computer animation, and cryptography among many others.
- Learn one of the mathematical subjects needed for Data Science.
- Learn a mathematical subject useful in becoming a Quant on Wall Street.

Requirements

- Basic understanding of algebra

Description

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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:

**Computer Science****Data Science****Actuarial Science****Financial Mathematics****Cryptography****Engineering****Computer Graphics****Economics**

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:

**Gaussian elimination****Vectors****Matrix Algebra****Determinants****Vector Spaces****Subspaces**

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!**

Who is the target audience?

- Working Professionals
- Anyone interested in gaining mastery of the core concepts in Linear Algebra.
- Adult Learners
- College Students

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Curriculum For This Course

Expand All 90 Lectures
Collapse All 90 Lectures
08:02:12

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Introduction
1 Lecture
03:44

Preview
03:44

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Solving Systems of Linear Equations
10 Lectures
47:13

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.

Gaussian Elimination

11:13

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.

Gaussian Elimination and Row Echelon Form

18:15

Practice problems for Gaussian elimination

Problem Set Gaussian Elimination

1 page

Solutions to Problem set Gaussian elimination

Solutions to Problem set Gaussian elimination

1 page

Detailed solutions are provided if needed.

Detailed Solutions to Problem Set Gaussian Elimination

3 pages

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.

Preview
11:13

An additional example of applying row operations is provided.

Elementary Row Operations: Additional Example

06:32

Practice problems for Elementary Row Operations

Preview
1 page

Solutions to Problem set Elementary Row Operations

Solutions to Problem Set Elementary Row Operations

1 page

Detailed solutions to the problem set Elementary Row Operations are provided, if needed.

Detailed Solutions to Problem Set Elementary Row Operations

4 pages

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Vectors
10 Lectures
57:17

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.

Vector Operations and Linear Combinations

18:57

Practice problems for Vector Operations and Linear Combinations

Problem Set Vector Operations and Linear Combinations

2 pages

Solutions to Problem set Vector Operations and Linear Combinations

Solutions to Problem Set Vector Operations and Linear Combinations

1 page

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.

Vector Equations and the Matrix Equation Ax=b.

16:16

The notion of linear independence is introduced.

Linear Independence

06:26

An example of determining linear independence is provided.

Students will learn how to determine when a set of vectors is linearly independent.

Preview
11:02

A second example of determining linear independence is provided.

Students will learn how to determine when a set of vectors is linearly independent.

Linear Independence: Example 2

04:36

Practice problems for Linear Independence

Problem Set Linear Independence

1 page

Solutions to Problem set Linear Independence

Solutions to Problem Set Linear Independence

1 page

Detailed solutions to problem set Linear Independence are provided, if needed.

Detailed Solutions to Problem Set Linear Independence

2 pages

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Matrix Operations
5 Lectures
16:30

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.

Addition and Scalar Multiplication

07:12

The matrix operation of multiplication is introduced.

Students will learn how to multiply two matrices.

Multiplication

09:18

Practice problems for Matrix Operations

Problem Set Matrix Operations

1 page

Solutions to Problem set Matrix Operations

Solutions to Problem Set Matrix Operations

1 page

Review Request

1 page

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Properties of Matrix Addition and Scalar Multiplication
9 Lectures
34:20

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.

Commutativity, Associativity, and Distributivity

13:13

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.

Identities, Additive Inverses, Multiplicative Associativity and Distributivity

14:25

Practice problems for Properties of Matrix Operations

Problem Set Properties of Matrix Operations

1 page

Solutions to Problem Set Properties of Matrix Operations

Solutions to Problem Set Properties of Matrix Operations

1 page

Detailed solutions to problem set Properties of Matrix Operations is provided, if needed.

Detailed Solutions to Problem Set Properties of Matrix Operations

3 pages

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.

Transpose of a Matrix

06:42

Practice problems for Transpose of a Matrix.

Problem Set Transpose of a Matrix

1 page

Solutions to Problem Set Transpose of a Matrix

Solutions to Problem Set Transpose of a Matrix

1 page

Detailed solutions to Problem Set Transpose of a Matrix are provided, if needed.

Detailed Solutions to Problem Set Transpose of a Matrix

1 page

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The Inverse of a Matrix
6 Lectures
22:29

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.

Preview
05:30

The process of Gauss-Jordan Elimination is explained.

Students will learn how to find the inverse of a matrix using Gauss-Jordan Elimination.

Gauss-Jordan Elimination

10:56

An additional example of Gauss-Jordan Elimination is provided.

Gauss-Jordan Elimination: Additional Example

06:03

Practice problems for Inverse of a Matrix

Problem Set Inverse of a Matrix

1 page

Solutions to Problem Set Inverse of a Matrix

Solutions to Problem Set Inverse of a Matrix

1 page

Detailed solutions to Problem set Inverse of a Matrix are provided, if needed.

Detailed Solutions to Problem Set Inverse of a Matrix

5 pages

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Determinants
7 Lectures
15:43

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.

Determinant of a 2 by 2 Matrix

02:34

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.

Cofactor Expansion

07:18

Additional examples of cofactor expansion are provided.

Cofactor Expansion: Additional Examples

05:51

Practice problems for Determinants

Problem Set Determinants

1 page

Solutions to Problem Set Determinants

Solutions to Problem Set Determinants

1 page

Detailed solutions to Problem set Determinants are provided, if needed.

Detailed Solutions to Problem Set Determinants

2 pages

Review Request

1 page

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Properties of Determinants
6 Lectures
22:08

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.

Determinant of a Product of Matrices and of a Scalar Multiple of a Matrix

11:07

The relationship between determinants and invertibility is explained.

Students will be able to determine when a matrix is invertible by examining the determinant.

Determinants and Invertibility

07:26

The determinant of the transpose of a matrix is discussed.

Students will learn how to find the determinant of the transpose of a matrix.

Determinant of the Transpose of a Matrix

03:35

Practice problems for Properties of Determinants

Preview
1 page

Solutions to Problem set Properties of Determinants

Preview
1 page

Detailed solutions to Problem set Properties of Determinants are provided, if needed.

Detailed Solutions to Problem Set Properties of Determinants

2 pages

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Vector Spaces
10 Lectures
01:00:21

The definition of vector space is explained.

Students will learn what a vector space is.

Preview
07:22

A proof is given to show that R2 is a vector space.

Students will learn how to prove a set is a vector space.

Vector Space Example

13:43

The proof of the claim that R2 is a vector space is continued.

Vector Space Example Continued

12:18

An additional example of a vector space is provided.

Vector Space Additional Example

16:46

The proof of the first five properties of a vector space applied to P2 is continued.

Vector Space Additional Example Continued

04:03

Practice problems for Vector Spaces.

Problem Set Vector Spaces

1 page

Solutions to Problem Set Vector Spaces

Solutions to Problem Set Vector Spaces

4 pages

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.

Examples of Sets that are Not Vector Spaces

06:09

Practice problems for Sets that are not vector spaces.

Problem Set Sets That Are Not Vector Spaces

1 page

Solutions to Problem set Sets that are not vector spaces.

Solutions to Problem Set Sets that are not vector spaces

2 pages

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Subspaces
9 Lectures
32:28

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.

Preview
09:55

The definition of a trivial subspace and of a nontrivial subspace are provided.

Definition of Trivial and Nontrivial Subspace

03:38

An example of a subspace of M(2,2), the set of all 2 by 2 matrices, is provided.

Additional Example of Subspace

05:17

Practice problems for Subspaces

Problem Set Subspaces

1 page

Solutions to Problem Set Subspaces

Solutions to Problem Set Subspaces

2 pages

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.

Subsets that are Not Subspaces

09:13

An additional example of a subset that is not a subspace is discussed.

Subsets that are Not Subspaces: Additional Example

04:25

Practice problems for Subsets that are not subspaces.

Problem Set Subsets that are not subspaces

1 page

Solutions to Problem Set Subsets that are not subspaces.

Solutions to Problem Set Subsets that are not subspaces

1 page

3 More Sections

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About the Instructor

PhD in Mathematics

*Philosophy of Language: Solidify Critical Thinking Skills* and *Linear Algebra for Beginners: Open Doors to Great Careers*.

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