If $\displaystyle \left[\begin{array}{rr}3 & -1 \\ 0 & 1 \\ 2 & -3\end{array}\right] \mathrm{A}=\left[\begin{array}{r}2 \\ -5 \\ -17\end{array}\right]$, then find matrix A .

Let $\displaystyle \mathrm{A}=\left[\begin{array}{l}x \\ y\end{array}\right] \Rightarrow\left[\begin{array}{cc} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}2 \\ -5 \\ -17\end{array}\right]$ \[\Rightarrow 3 x-y=2, y=-5 \text { and } \] Put the values in $\displaystyle 2 x-3 y=-17$, L.H.S. $\displaystyle =2(-1)-3(-5) \neq-17=$ R.H.S. ∴ The matrix ' $\displaystyle \mathrm{A}$ ' does not exist.