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Spring 2014 Math 601 Name: Quiz 5 Question 1. (10 pts) Let F : R2 → R2 be the linear transformation defined by F (x, y) = (−3x + 4y, 4x + 3y). Find the matrix representation of F with respect to the basis S = {u1 , u2 } = {(1, 2), (−2, 1)}. Solution: with respect to the basis S = {u1 , u2 } = {(1, 2), (−2, 1)}, we have 5 [F (u1 )]S = 0 0 [F (u2 )]S = −5 5 0 So [F ]S = 0 −5 1 Question 2. (10 pts) Consider the vector space P2 (t). Choose a basis S = {1, t, t2 }. Let T be the linear transformation defined by T (f ) = f 00 + 4f 0 . Find the matrix representation of T relative to the basis S. Solution: So 0 [T (1)]S = 0 0 4 [T (t)]S = 0 0 2 [T (t2 )]S = 8 0 0 4 2 [T ]S = 0 0 8 0 0 0 2