Overview:

1. Introduction to matrices
2. Adding and subtracting matrices
3. Multiplying matrices
4. 2 × 2 Matrices and linear transformations
5. Determinants of 2 × 2 matrices
6. Inverses of 2 × 2 matrices
7. Invariant points and lines in 2 dimensions
8. 3 × 3 Matrices and linear transformations
9. Determinants of 3 × 3 matrices
10. Inverses of 3 × 3 matrices
11. Matrices and simultaneous equations

An invariant point under a transformation is a point that maps to itself. As noted in part 4, linear transformations map the origin to the origin, so the origin is always an invariant point under a linear transformation.

An invariant line is a line that maps to itself. To be precise, every point on the invariant line maps to a point on the line itself. Note that the point needn’t map to itself.

A a line of invariant points is a line where every point every point on the line maps to itself. Any line of invariant points is therefore an invariant line, but an invariant line is not necessarily always a line of invariant points.

Use this applet to see invariant points, invariant lines, and lines of invariant points for three examples of linear transformations.