Question

Find x and y, if : ${\displaystyle \left[\begin{array}{cc}x& 3x\\ y& 4y\end{array}\right]\left[\begin{array}{c}2\\ 1\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]}$.

Answer 1

${\displaystyle \left[\begin{array}{cc}x& 3x\\ y& 4y\end{array}\right]\left[\begin{array}{c}2\\ 1\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]}$

${\displaystyle \Rightarrow \left[\begin{array}{c}x\times 2+3x\times 1\\ y\times 2+4y\times 1\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]}$

${\displaystyle \Rightarrow \left[\begin{array}{c}2x+3x\\ 2y+4y\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]}$

${\displaystyle \Rightarrow \left[\begin{array}{c}5x\\ 6y\end{array}\right]=\left[\begin{array}{c}5\\ 12\end{array}\right]}$

Comparing the corresponding elements, we get

5x = 5 ${\displaystyle \Rightarrow }$ x = 1

6y = 12 ${\displaystyle \Rightarrow }$ y = 2