Given that \(P = \begin{pmatrix} y – 2 & y – 1 \\ y – 4 & y + 2 \end{pmatrix}\) and |P| = -23, find the value of y.
- -4
-
-3
- -1
- 2
The correct answer is: B
Explanation
\(P = begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\)
\(|P| = (y - 2)(y + 2) - (y - 1)(y - 4) = (y^{2} - 4) - (y^{2} - 5y + 4) = -23\)
\(5y - 8 = -23 \implies 5y = -23 + 8 = -15\)
\(y = \frac{-15}{5} = -3\)