Question

In Problems $7-14$, find the value of each determinant.

$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|$

Short answer

The value of the determinant$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|$is,$4$.

Step-by-step solution

Step 1 Given determinant is,

$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|$

Evaluate the given determinant.

$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|=6\left(-1\right)-5\left(-2\right)$

Step 2 Now simplify it.

$$\begin{gathered} \left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|=-6+10 \\ =4 \end{gathered}$$

Thus, the value of the determinant$\left|\begin{array}{cc}6& 5\\ -2& -1\end{array}\right|$is,$4$.