Question 4. Let L: R → R be a linear transformation in the Euclidean space defined by L(¤1, x2) = (5x1 + 2x2, –3x1 + 2x2)". (a) Find the matrix [L]ST relative to the bases S = {(1,2)", (1, –1)"} and T = {(1,0), (1, 1)} (b) Find the coordinate vectors [(3, 4)"]s, [L(3, 4)]T and then use [L]sT to find L(3, 4). Verify the last result by computing L(3, 4) directly.

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