Linear Transformation Questions

Question

Suppose that T : R² -> R² is a linear transformation satisfying T(e₁) = (5, 4) and T(e₂) = (3, -2). Compute the following:

(a) T(2, 0)

(b) T(1, 1)

(c) T(2, -3)

Answer 1

Matrix T is 2×2 matrix : 1st column is T(e₁) = (5, 4); 2nd column of T is T(e₂) = (3, -2). Now we have:

(a) T(2,0) = (5·2 + 3·0, 4·2 - 2·0) = (10, 8)

(b) T(1, 1) = (5·1 + 3·1, 4·1 - 2 ·1) = (8, 2)

(c) T(2, -3) = (5·2 + 3·(-3),4·2 -2·(-3)) = (1, 14)