Question

Find x and y if $\left(\begin{array}{cc}2x& 0\\ 0& 3y\end{array}\right)$ is a scalar matrix whose diagonal element is 12

• A. x = 6, y = 4
• B. x = 4, y = 6
• C. x = 12, y = 12
• D. x = -6, y = -4

Answer 1

The correct option is A

x = 6, y = 4

$\left(\begin{array}{cc}2x& 0\\ 0& 3y\end{array}\right)=\left(\begin{array}{cc}12& 0\\ 0& 12\end{array}\right)$ (given)
$\Rightarrow 2x=12$ and $3y=12$
$\Rightarrow$ $x=6$ and $y=4$