First slide

Operations of matrix

Question

Find non-zero value of $x$ satisfying the matrix equation
$x [\begin{matrix} 2 x & 2 \\ 3 & x \end{matrix}] + 2 [\begin{matrix} 8 & 5 x \\ 4 & 4 x \end{matrix}] = 2 [\begin{matrix} x^{2} + 8 & 24 \\ 10 & 6 x \end{matrix}]$

Very Easy

A

1
B

2
C

3
D

4

Solution

$\begin{matrix} x [\begin{matrix} 2 x & 2 \\ 3 & x \end{matrix}] + 2 [\begin{matrix} 8 & 5 x \\ 4 & 4 x \end{matrix}] = 2 [\begin{matrix} x^{2} + 8 & 24 \\ 10 & 6 x \end{matrix}] \\ [\begin{matrix} 2 x^{2} & 2 x \\ 3 x & x^{2} \end{matrix}] + [\begin{matrix} 16 & 10 x \\ 8 & 8 x \end{matrix}] = [\begin{matrix} 2 x^{2} + 16 & 48 \\ 20 & 12 x \end{matrix}] \\ [\begin{matrix} 2 x^{2} + 16 & 12 x \\ 3 x + 8 & x^{2} + 8 x \end{matrix}] = [\begin{matrix} 2 x^{2} + 16 & 48 \\ 20 & 12 x \end{matrix}] \\ 12 x = 48 \\ x = 4 \end{matrix}$

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