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