Question

Solve for x.


`\left[\begin{array}{ccc}5&2\\3&x\\\end{array}\right] =x^2`

Answer 1

`\begin{bmatrix} 5&2\\ 3&x \end{bmatrix}~~ = ~~x^2\implies \stackrel{ \textit{determinant of a }2* 2 ~matrix}{(5)(x)~~ - ~~(3)(2)}~~ = ~~x^2\implies 5x-6=x^2 \\\\\\ 0=x^2-5x+6\implies 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}`