Question

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

$\left[\begin{array}{cc}-2& 0\\ 7& -5\end{array}\right]$

Short answer

The value of the determinant is$10.$

Step-by-step solution

Step 1. Given information 

The given square matrix is

$\left[\begin{array}{cc}-2& 0\\ 7& -5\end{array}\right]$

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

$$\begin{gathered} =(-2)(-5)-\left(7\right)\left(0\right) \\ =\left(10\right)-\left(0\right) \\ =10 \end{gathered}$$