Question:
If $\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$, find $x, y$ and $z$
Solution:
Here,
$\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{c}x \\ -y \\ -z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$
$\therefore x=1, y=0$ and $z=-1$