If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.
- \(3\frac{8}{9}\)
-
\(3\)
- \(2\frac{1}{2}\)
- \(2\)
The correct answer is: B
Explanation
\(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\)
\((m^{2} - 4m + 4) - (m^{2} + 5m + 4) = -27\)
\(-9m = -27 \implies m = 3\)