Tutorial 3 Solutions

Tutorial 3 Solutions - Tutorial 3, Solution MATH 1104...

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Tutorial 3, Solution MATH 1104 1-Last name: First name: 2-Last name: First name: 3-Last name: First name: 4-Last name: First name: 5-Last name: First name: ——————————————————————————— 1. Let T be a transformation from R 5 to R 5 given by: T x 1 x 2 x 3 x 4 x 5 = 9 x 1 + 13 x 2 + 5 x 3 + 6 x 4 - x 7 14 x 1 + 15 x 2 - 7 x 3 - 6 x 4 + 4 x 5 - 8 x 1 - 9 x 2 + 12 x 3 - 5 x 4 - 9 x 5 - 5 x 1 - 6 x 2 - 8 x 3 + 9 x 4 + 8 x 5 13 x 1 + 14 x 2 + 15 x 3 + 2 x 4 + 11 x 5 a: Find the standard matrix of T . b: Determine if T is one-to-one, justify your answer. c: Determine if t is onto, justify your answer. Solution: (a): A = 9 13 5 6 - 1 14 15 - 7 - 6 4 - 8 - 9 12 - 5 - 9 - 5 - 6 - 8 9 8 13 14 15 2 11 . (b): The REF form of A is B = 1 0 0 0 5 0 1 0 0 - 4 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 , there is no pivot last column so T is not one-to one, (c): There is no pivot in each row of B, so T is not onto. ———————————————————————————
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This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Fall '10 term at Carleton.

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