Find non-zero values of x satisfying the matrix equation $x\begin{bmatrix}2x&2\\3&x\end{bmatrix}+2\begin{bmatrix}8&5x\\4&4x\end{bmatrix}=2\begin{bmatrix}x^2+8&24\\10&6x\end{bmatrix}$.
Answer & explanation
Correct answer: option 1
Given that
$x\begin{bmatrix}2x&2\\3&x\end{bmatrix}+2\begin{bmatrix}8&5x\\4&4x\end{bmatrix}=2\begin{bmatrix}x^2+8&24\\10&6x\end{bmatrix}$
$⇒\begin{bmatrix}2x^2&2x\\3x&x^2\end{bmatrix}+\begin{bmatrix}16&10x\\8&8x\end{bmatrix}=\begin{bmatrix}2x^2+16&47\\20&12x\end{bmatrix}$
$⇒\begin{bmatrix}2x^2+16&2x+10x\\3x+8&x^2+8x\end{bmatrix}=\begin{bmatrix}2x^2+16&47\\20&12x\end{bmatrix}$
Comparing the elements, we get
$2x+10x=48$
$⇒12x=48$
$⇒x=4$
This value of x also satisfies the equations $3x+8=20$ and $x^2 + 8x = 12x$.