Linear algebra starts with a look at systems of equations and ends up being a study of vectors and vector spaces. While these ideas seem like they aren’t connected, you slowly begin to see the connections as you delve deeper into the topic. The lessons below will get you started.

## Working with matrices

- Matrix notation and the size of a matrix
- Adding and subtracting matrices, and multiplying a matrix by a constant
- Multiplying matrices (includes animation of the process)
- Multiplying matrices on the TI83 or 84 calculator

- The identity matrix

- What is an inverse matrix?

## Systems of linear equations

- Augmented matrices and systems of linear equations
- Row operations
- Row reduction with the TI 83/84 calculator
- General solutions to systems of equations

## Vectors

- Linear combinations of vectors – the basics
- How to determine if a vector is a linear combination of other vectors

## Transformations

- Introduction to linear transformations
- Showing a transformation is linear using the definition
- Matrix transformations
- Proof that every matrix transformation is a linear transformation
- The standard matrix of a linear transformation