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Winter 2006 - Nagy's Class - Exam 2 (Version A)

Winter 2006 - Nagy's Class - Exam 2 (Version A) - Print...

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Print Name: Student Number: Section Time: Math 20F. Midterm Exam 2 March 8, 2006 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (9 points) Consider the linear transformations T : IR 3 IR 3 and S : IR 3 IR 3 given by T x 1 x 2 x 3 = 2 x 1 - x 2 + 3 x 3 - x 1 + 2 x 2 - 4 x 3 x 2 + 3 x 3 , S x 1 x 2 x 3 = - x 1 2 x 2 3 x 3 (a) Find a matrix A associated to T and the matrix B associated to S . Show your work. (b) Is T one-to-one? Is T onto? Justify your answer. (c) Find the matrix of the composition T S : IR 3 IR 3 . Justify your answer. (a) Let A = [ T ( e 1 ) , T ( e 2 ) , T ( e 3 )] and B = [ S ( e 1 ) , S ( e 2 ) , S ( e 3 )]. Then, A = 2 - 1 3 - 1 2 - 4 0 1 3 , B = - 1 0 0 0 2 0 0 0 3 . (b) 2 - 1 3 - 1 2 - 4 0 1 3 1 - 2 4 2 - 1 3 0 1 3 1 - 2 4 0 3 5 0 1 3

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