Question

If A = $\left[\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right]$, B = $\left[\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right]$, find matrix X such that 2A + 3X = 5B.

Answer 1

$$\begin{gathered} \mathrm{Given}:2A+3X=5B \\ \Rightarrow 2\left[\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right]+3X=5\left[\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right] \\ \Rightarrow \left[\begin{array}{cc}4& -4\\ 8& 4\\ -10& 2\end{array}\right]+3X=\left[\begin{array}{cc}40& 0\\ 20& -10\\ 15& 30\end{array}\right] \\ \Rightarrow 3X=\left[\begin{array}{cc}40& 0\\ 20& -10\\ 15& 30\end{array}\right]-\left[\begin{array}{cc}4& -4\\ 8& 4\\ -10& 2\end{array}\right] \\ \Rightarrow 3X=\left[\begin{array}{cc}40-4& 0+4\\ 20-8& -10-4\\ 15+10& 30-2\end{array}\right] \\ \Rightarrow 3X=\left[\begin{array}{cc}36& 4\\ 12& -14\\ 25& 28\end{array}\right] \\ \Rightarrow X=\frac{1}{3}\left[\begin{array}{cc}36& 4\\ 12& -14\\ 25& 28\end{array}\right] \\ \Rightarrow X=\left[\begin{array}{cc}12& \frac{4}{3}\\ 4& \frac{-14}{3}\\ \frac{25}{3}& \frac{28}{3}\end{array}\right] \end{gathered}$$