Q. 52 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 51–56, solve for x, 

$\left|\begin{array}{ll}x& 1\\ 3& x\end{array}\right|=-2$

Step-by-Step Solution

Answer

The value of x is $\pm 1$.

Step 1. Given Information

We are given, 

$\left|\begin{array}{ll}x& 1\\ 3& x\end{array}\right|=-2$

We have to find the value of x.

Step 2. Solving the determinant

 Solving the determinant, we get 

$$\begin{gathered} \left|\begin{array}{ll}x& 1\\ 3& x\end{array}\right|=-2 \\ x\left(x\right)-1\left(3\right)=-2 \\ {x}^2-3=-2 \\ {x}^2=1 \\ x=\pm 1 \end{gathered}$$