Q70. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

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