Question

Solve the equation of x,y, z and t, if $2\left[\begin{array}{cc}x& z\\ y& t\end{array}\right]+3\left[\begin{array}{cc}1& -1\\ 0& 2\end{array}\right]=3\left[\begin{array}{cc}3& 5\\ 4& 6\end{array}\right]$

Answer 1

Given, $2\left[\begin{array}{cc}x& z\\ y& t\end{array}\right]+3\left[\begin{array}{cc}1& -1\\ 0& 2\end{array}\right]=3\left[\begin{array}{cc}3& 5\\ 4& 6\end{array}\right]\Rightarrow \left[\begin{array}{cc}2x& 2z\\ 2y& 2t\end{array}\right]+\left[\begin{array}{cc}3& -3\\ 0& 6\end{array}\right]=\left[\begin{array}{cc}9& 15\\ 12& 18\end{array}\right]\Rightarrow \left[\begin{array}{cc}2x+3& 2z-3\\ 2y+0& 2t+6\end{array}\right]=\left[\begin{array}{cc}9& 15\\ 12& 18\end{array}\right]$
By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
2x+3 =9, 2y+0=12, 2z-3 =15 and 2t+6=18

$\Rightarrow x=\frac{9-3}{2},y=\frac{12}{2},z=\frac{15+3}{2}andt=\frac{18-6}{2}$
$\Rightarrow x=3,y=6,z=9$ and t=6.