Given that p = \(\begin{pmatrix} m + 1 & m – 1 \\ m + 4 & m – 8 \end{pmatrix}\) and |p| = – 34, find the value of m.
- 5
- 4
-
3
- 2
The correct answer is: C
Explanation
Given: p = \(\begin{pmatrix} m + 1 & m - 1 \\ m + 4 & m - 8 \end{pmatrix}\) and |p| = -32,
But the determinant of p = -32
[{(m + 1)(m - 8)} - {(m - 1)(m + 4)}] = - 34
[m\(^2\) - 8m + m - 8)] - [( m\(^2\) + 4m - m - 4] = - 34
[m\(^2\) - 7m - 8] - [m\(^2\) + 3m - 4] = -34
m\(^2\) - 7m - 8 - m\(^2\) - 3m + 4 = - 34
- 7m - 3m - 4 = - 34
- 10m = - 34 + 4 = - 30
m = \(\frac{-30}{-10}\) = 3
Hence, m = 3