Question

In Problems 51–56, solve for x,

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

Short answer

The value of xis $\pm 1$.

Step-by-step solution

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

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