Solve this

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 $z=1$

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