Question

If $\left[\begin{array}{ccc}1& 0& 0\\ 0& y& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ -1\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$, find x, y and z.

Answer 1

$$\begin{gathered} \text{Here,} \\ \left[\begin{array}{ccc}1& 0& 0\\ 0& y& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ -1\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right] \\ \Rightarrow \left[\begin{array}{c}x\\ -y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right] \\ \therefore x=1,y=0\mathrm{and}z=1 \end{gathered}$$