Question

evaluate the determinant.\

$$\begin{vmatrix}-5&0\\\\-8&7\\end{vmatrix}$$

Explanation:

Step1: Recall the formula for the determinant of a 2x2 matrix \(

$$\begin{vmatrix}a&b\\c&d\end{vmatrix}$$

=ad - bc\)
For the given matrix \(

$$\begin{vmatrix}-5&0\\-8&7\end{vmatrix}$$

\), we have \(a = -5\), \(b = 0\), \(c = -8\), \(d = 7\).

Step2: Substitute the values into the formula

\(ad - bc=(-5)\times7 - 0\times(-8)\)

Step3: Calculate each term

\((-5)\times7=-35\) and \(0\times(-8) = 0\)

Step4: Subtract the two terms

\(-35-0=-35\)

Answer:

\(-35\)