Determinant of a Transformed Matrix
A linear transformation T: R² → R² is defined by its effect on the standard basis vectors: T(e₁) = (3, 1) and T(e₂) = (2, -4). Let P be the 2×2 matrix with columns p = (5, -2) and q = (1, 3). What is the determinant of the matrix whose columns are the transformed vectors T(p) and T(q)?
A
143
B
-65
C
65
D
-238
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