Chapter 11.3, Problem 54AYU

solve for x.

$\left[\begin{array}{c}3\\ 1\\ 0\end{array}\begin{array}{c}2\\ x\\ 1\end{array}\begin{array}{c}4\\ 5\\ -2\end{array}\right]=0$

To determine

To find: The solution for $x$ where, $\left|\begin{array}{ccc}3& 2& 4\\ 1& x& 5\\ 0& 1& -2\end{array}\right|=0$.

Answer to Problem 54AYU

$x=-\frac{7}{6}$

Explanation of Solution

Given:

$\left|\begin{array}{ccc}3& 2& 4\\ 1& x& 5\\ 0& 1& -2\end{array}\right|=0$

Calculation:

$\left|\begin{array}{ccc}3& 2& 4\\ 1& x& 5\\ 0& 1& -2\end{array}\right|=0$

$3\cdot \left(-2x-5\right)-2\cdot \left(-2-0\right)+4\cdot \left(1-0\right)=0$

$-6x-15+4+4=0$

$-6x-7=0$

$6x+7=0$

$6x=-7$

$x=-\frac{7}{6}$