If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.
Question 1 Report
If \(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = -27\), find the value of m.
Answer Details
The determinant of a 2x2 matrix is given by the formula:
\(\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc\)
Using this formula, we can find the determinant of the given matrix:
\(\begin{vmatrix} m-2 & m+1 \\ m+4 & m-2 \end{vmatrix} = (m-2)(m-2) - (m+1)(m+4)\)
Simplifying this expression, we get:
\((m-2)^2 - (m+1)(m+4) = m^2 - 4m + 4 - (m^2 + 5m + 4) = -9m\)
Setting this equal to the given determinant of -27, we have:
\(-9m = -27\)
Solving for m, we get:
\(m = 3\)
Therefore, the answer is: \(3\).
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