Q42. - Algebra 2

Question

Find the value of each determinant.

42.

$\left|\begin{array}{cc}\mathbf{3}& \mathbf{2}\\ \mathbf{-}\mathbf{2}& \mathbf{4}\\ & \end{array}\right|$

Step-by-Step Solution

Answer

The value of the given determinant is 16.

Step 1 ­- Description of step.

The value of a second-order determinant can be found out by calculating difference of product of two diagonals.

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

Step 2 ­- Find the value of the determinant.

The value of the determinant $\left|\begin{array}{cc}3& 2\\ -2& 4\end{array}\right|$is given by:

$\begin{array}{c}\left|\begin{array}{cc}3& 2\\ -2& 4\end{array}\right|=\left(3\right)\left(4\right)-\left(-2\right)\left(2\right)\\ =12-\left(-4\right)\\ =12+4\\ =16\end{array}$

Step 3 ­- Description of step.

The value of the given determinant is 16.