AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.13 Matrices as Functions
Notes
A matrix acts like a function on vectors.
- Composing transformations means multiplying matrices: apply $B$ then $A$ is $AB$.
- The inverse matrix undoes the transformation.
Practice
Apply $B$ first, then $A$. The single matrix is:
The matrix nearest the vector acts first.
A transformation with $\det=0$:
Area scale factor 0.
A transformation scales area by 3. Its determinant could be:
$|\det|=3$; the negative sign means a flip.
Ready for more? Take the Unit 4 test.