Mathematics - Matrices Question with Solution | TestHub

Let $\mathrm{A}=\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}y\\ x\\ 1\end{array}\right]$ $$\begin{array}{rl}& \mathrm{AB}=\left[\begin{array}{ccc}1& 2& x\\ 3& -1& 2\end{array}\right]\left[\begin{array}{l}y\\ x\\ 1\end{array}\right]\\ & \Rightarrow \left[\begin{array}{l}6\\ 8\end{array}\right]=\left[\begin{array}{l}y+2x+x\\ 3y-x+2\end{array}\right]\\ & \Rightarrow \left[\begin{array}{l}6\\ 8\end{array}\right]=\left[\begin{array}{l}y+3x\\ 3y-x+2\end{array}\right]\\ & \Rightarrow y+3x=6\text{ and }3y-x=6\end{array}$$ On solving, we get $$\begin{array}{rl}& x=\frac{6}{5}\text{ and }y=\frac{12}{5}\\ & \Rightarrow y=2x\end{array}$$