Q 233 - Intermediate Algebra

Question

In the following exercises, evaluate the determinate of each square matrix. 

$\left[\begin{array}{cc}-4& 8\\ -3& 5\end{array}\right]$

Step-by-Step Solution

Answer

The value of the determinant is $4.$

Step 1. Given information

The given square matrix is 

$\left[\begin{array}{cc}-4& 8\\ -3& 5\end{array}\right]$

We have to evaluate the determinate of a given square matrix. 

Step 2. To find the determinant, multiply the diagonals of the matrix and then subtract them.

The determinant of the matrix is 

$$\begin{gathered} =(-4)\left(5\right)-\left(8\right)(-3) \\ =(-20)-(-24) \\ =-20+24 \\ =4 \end{gathered}$$