Question

Find non-zero values of x satisfying the matrix equation :

$x\left[\begin{array}{cc}2x& 2\\ 3& x\end{array}\right]+2\left[\begin{array}{cc}8& 5x\\ 4& 4x\end{array}\right]=2\left[\begin{array}{cc}{x}^2+8& 24\\ 10& 6x\end{array}\right]$

• A. 1
• B. 4
• C. 2
• D. 5

Answer 1

Answer: (B)

4

Given,

$x\left[\begin{array}{cc}2x& 2\\ 3& x\end{array}\right]+2\left[\begin{array}{cc}8& 5x\\ 4& 4x\end{array}\right]=2\left[\begin{array}{cc}{x}^2+8& 24\\ 10& 6x\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}2x^2+16& 2x+10x\\ 3x+8& x^2+8x\end{array}\right]=\left[\begin{array}{cc}2x^2+16& 48\\ 20& 12x\end{array}\right]$

By equality of matrices,

$2x+10x=48$, $3x+8=20$ and $x^2+8x=12x$

$12x=48,3x=12$ and $x^2-4x=0$

$x=4,x(x-4)=0$

$x=0,4$

Non-zero value of $x$ satisfying the given matrix equation

$x=4$