APFIVE Determinant of a Transformed Matrix
A linear transformation T: R² → R² maps the standard basis vectors as follows: T(e₁) = (3, 1) and T(e₂) = (2, -4). If vectors p = (5, -2) and q = (1, 3) are represented as columns of a 2×2 matrix P, what is the determinant of the matrix representing T(P)?
A
143
B
-238
C
-65
D
65
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