Answer
$x=-4$
Work Step by Step
We find the determinant of the given matrix as follows:
$\begin{vmatrix} -2 & 0 &1 \\ -1 & 3 & x \\ 5 &-2 &0 \\ \end{vmatrix}$
$=-2[ (3)(0) -(-2)(x)] -0 +1[(-1)(-2) -(5)(3) ] $
$=-4x-13$
Substitute the expression of the determinant in the given equation:
$-4x-13=3$
Solve for $x$:
$-4x=16$
$x=-4$
The solution of the given equation is:
$x=-4$
