Given that (P = begin{pmatrix} y – 2 & y – 1 \ y – 4 & y + 2 end{pmatrix}) and |P| = -23, find the value of y.
-
A.
-4 -
B.
-3 -
C.
-1 -
D.
2
Correct Answer: Option 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)