Question

If $x\in N$ and $\lfloor \begin{array}{cc}x+3& -2\\ -3x& 2x\end{array}\rfloor =8$, then find the value of $x$.

Answer 1

Solving the above matrix we get : $(x+3)\left(2x\right)-(-3x)(-2)=8$

$\therefore$ $2x^2+6x-6x=8$

$2x^2=8$

$x^2=\frac{8}{2}=4$

$x=\sqrt{4}$

$x=\pm 2$

since $x\in N$ we have $x=2$