AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.11 The Inverse and Determinant of a Matrix
Notes
For $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$:
- $\det A=ad-bc$.
- If $\det A\ne0$: $\displaystyle A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$.
- $|\det A|$ is the area scale factor of the transformation.
Practice
$\det\begin{bmatrix}3&1\\2&4\end{bmatrix}=$
$12-2$.
A matrix has an inverse exactly when:
$\det=0$ means not invertible.
The inverse of $\begin{bmatrix}2&0\\0&4\end{bmatrix}$:
Reciprocals on the diagonal.
Ready for more? Take the Unit 4 test.