Q7. - Algebra 2

Question

Find the value of each determinant.

 

7. $\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|$

Step-by-Step Solution

Answer

The value of the determinant $\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|=-38$.

Step 1 - Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is.,  $\left|\begin{array}{cc}a& b\\ c& d\\ & \end{array}\right|=ad-bc$.

Step 2 - Find the determinant

Apply the definition of the method of finding determinant of second order matrix $\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|$.

$\left|\begin{array}{cc}7& 8\\ 3& -2\\ & \end{array}\right|=7\times \left(-2\right)-8\left(3\right)$

Step 3 - Simplify

To further simplify multiply the values first and then find the difference.

 

$\begin{array}{c}\left|\begin{array}{cc}7& 8\\ 3& -2\end{array}\right|=7\times (-2)-8\left(3\right)\\ =-14-24\\ =-38\end{array}$