Q6. - Algebra 2

Question

Find the value of each determinant.

5.

$\left|\begin{array}{cc}\mathbf{-}\mathbf{8}& \mathbf{3}\\ \mathbf{6}& \mathbf{5}\\ & \end{array}\right|$

Step-by-Step Solution

Answer

The value of the given determinant is $\mathbf{-}\mathbf{58}$.

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 $\left|\begin{array}{cc}-8& 3\\ 6& 5\end{array}\right|$is given by:

$\begin{array}{c}\left|\begin{array}{cc}-8& 3\\ 6& 5\end{array}\right|=\left(-8\right)\left(5\right)-\left(6\right)\left(3\right)\\ =-40-18\\ =-58\end{array}$

Step 3 ­- Description of step.

The value of the given determinant is $-58$.