Question

In the following exercise, evaluate the determinate of the square matrix.

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

Short answer

The determinant of the given matrix is $-4$.

Step-by-step solution

Step 1. Given information

The given matrix is:

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

Step 2. Finding the determinant of the matrix.

The determinant of the matrix is given as:

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

Thus, the determinant of the given matrix is $-4$