## Precalculus (6th Edition) Blitzer

The value of $x$ is, $=4$
Consider, $\left| \begin{matrix} 1 & x & -2 \\ 3 & 1 & 1 \\ 0 & -2 & 2 \\ \end{matrix} \right|=-8$ Evaluate the above determinant as follows: $\left| \begin{matrix} 1 & x & -2 \\ 3 & 1 & 1 \\ 0 & -2 & 2 \\ \end{matrix} \right|=-8$ Evaluate the above determinant by expanding along the first column as follows: $1\left| \begin{matrix} 1 & 1 \\ -2 & 2 \\ \end{matrix} \right|-3\left| \begin{matrix} x & -2 \\ -2 & 2 \\ \end{matrix} \right|+0=-8$ Next, calculate the above determinant as given: \begin{align} & 2-\left( -2 \right)-3\left( 2x-4 \right)=-8 \\ & 4-6x+12=-8 \\ & -6x+16=-8 \end{align} Add $-16$ to both sides to get, $-6x=-24$ Divide by $-6$. Now, $x=4$. Thus, $x=4$