A Few Matrix Applications
Example 2 (Matrix inverse):
Final step (solving the system):
If $b = \begin{bmatrix}3 \\ 7\end{bmatrix}$, then:
$x = A^{-1} b = \begin{bmatrix} 3 & -1 \\ -2 & 1 \end{bmatrix} \begin{bmatrix}3 \\ 7\end{bmatrix} = \begin{bmatrix} 9 - 7 \\ -6 + 7 \end{bmatrix} = \begin{bmatrix}2 \\ 1\end{bmatrix}$
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.