Evaluate the determinant: $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$
(18) To evaluate the determinant of a $2 \times 2$ matrix $\left|\begin{array}{cc}a & b \\ c & d\end{array}\right|$,we use the formula $ad - bc$.
Given the determinant $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$,we have $a=2, b=4, c=-5, d=-1$.
Substituting these values into the formula:
$= (2 \times -1) - (4 \times -5)$
$= -2 - (-20)$
$= -2 + 20$
$= 18$
Given the determinant $\left|\begin{array}{cc}2 & 4 \\ -5 & -1\end{array}\right|$,we have $a=2, b=4, c=-5, d=-1$.
Substituting these values into the formula:
$= (2 \times -1) - (4 \times -5)$
$= -2 - (-20)$
$= -2 + 20$
$= 18$
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