Question

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

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

Short answer

The value of the determinant is$4.$

Step-by-step solution

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

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