Question

Evaluate each determinant$\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|$.

Short answer

The determinant of$\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|=-6$ .

Step-by-step solution

Step 1. Write down the given information.

The given determinant to be evaluated is $\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|$.

Step 2. Concept used.

The determinant of $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$.

Step 3. Calculation.

The determinant of $\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|$ is evaluated as:$\begin{array}{c}\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|=(3\times -2)-(2\times 0)\\ =-6-0\\ =-6\end{array}$

Step 4. Conclusion.

The determinant of $\left|\begin{array}{cc}3& 0\\ 2& -2\end{array}\right|=-6$.