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# Introduction to Linear Algebra

## Matrices, vectors, and more - from theory to the real world!

Linear algebra is pervasive in just about all modern scientific subjects, including physics, mathematics, computer science, electrical engineering, economics, and aeronautical engineering. You’ll learn about its applications in computer graphics, signal processing, machine learning, RLC circuit analysis, and control theory.

By the end of this course, you’ll be able to solve systems of equations of all flavors and complexities using linear algebra, from a simple 2x2 matrix equation to much more complex systems involving many variables.

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1. 1

### Linear Equations

Multiple variables, multiple equations - no worries!

1. #### Two Linear Equations in Two Unknowns

Kick things off with a pair of equations in a pair of unknowns.

2. #### Three Unknowns

Increase the challenge with three equations in three unknowns.

3. #### Gaussian Elimination

Learn a general algorithm for solving systems of equations.

4. #### The Full Story of Gaussian Elimination

Look deeper into the math behind Gauss-Jordan reduction.

2. 2

### Vector Spaces

Explore the power of vectors with magic squares, spanning sets, and more...

1. Included with

#### Vector Spaces

What is the essence of a vector?

2. Included with

#### Subspaces and Span

Discover what it means to have a space within a space.

3. Included with

#### Linear Independence

Learn how to spot redundant vectors.

4. Included with

#### Basis and Dimension

What measures the size of a vector space?

3. 3

### Properties of Matrices

A fundamental building block for linear algebra.

1. Included with

#### Matrix Algebra

Find out what matrices and vectors share in common.

2. Included with

#### Inverses and Systems of Equations

Is it ever OK to divide by a matrix?

3. Included with

#### Four Fundamental Subspaces

See what the column, row, null and transpose kernel spaces have to say about a matrix.

4. Included with

Practice fundamental matrix concepts on a graph theory application.

4. 4

### Linear Maps and Matrices

Determinants, maps, bases, and more.

1. Included with

#### Linear Transformations

Learn how to turn vectors into... other vectors.

2. Included with

#### Properties of Linear Transformations

Uncover the deep connection between linear transformations and matrices.

3. Included with

#### 2x2 Determinants

Discover a simple test for matrix invertibility.

4. Included with

#### Determinants in Higher Dimensions

Explore some beautiful and useful properties of determinants.

5. 5

### Eigenvalues and Diagonalizability

Eigenvalues, eigenvectors, and applications!

1. Included with

#### Eigenvalues and Eigenvectors

Learn to work with special vectors of fundamental importance.

2. Included with

#### Characteristic Polynomial

Learn a surefire way to find eigenvalues.

3. Included with