Question

If $\left[\begin{array}{ccc}9& -1& 4\\ -2& 1& 3\end{array}\right]=A+\left[\begin{array}{ccc}1& 2& -1\\ 0& 4& 9\end{array}\right]$, then find matrix A.

Answer 1

$$\begin{gathered} \left[\begin{array}{ccc}9& -1& 4\\ -2& 1& 3\end{array}\right]=A+\left[\begin{array}{ccc}1& 2& -1\\ 0& 4& 9\end{array}\right] \\ \Rightarrow A=\left[\begin{array}{ccc}9& -1& 4\\ -2& 1& 3\end{array}\right]-\left[\begin{array}{ccc}1& 2& -1\\ 0& 4& 9\end{array}\right] \\ =\left[\begin{array}{ccc}9-1& -1-2& 4+1\\ -2-0& 1-4& 3-9\end{array}\right] \\ =\left[\begin{array}{ccc}8& -3& 5\\ -2& -3& -6\end{array}\right] \\ \mathrm{Hence},\mathrm{the}\mathrm{matrix}A=\left[\begin{array}{ccc}8& -3& 5\\ -2& -3& -6\end{array}\right]. \end{gathered}$$