## Chapter 3 Linear Transformations

ΒΆ###### Objectives

- Understand linear transformations both algebraically and graphically.
- Be able to perform basic matrix operations.
- Be able to connect ideas about one-to-one and onto transformations with systems of equations.
- Be able to connect ideas about kernels and images with null spaces and column spaces.
- Be able to calculate orthogonal projections onto a subspace.
- See how to use a computer algebra system to help perform basic operations and apply linear algebra to data analysis in a basic way.

In this unit we will explore how we can transform one vector spaces into another.