tut7 - (2 , 2) that includes 1 2 3 4 , 4 3 2 1 . 4: Let V...

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Math 136 Tutorial 7 Problems 1: a) Verify that B = { (1 , 0 , 1) , (1 , - 1 , 2) , ( - 1 , - 1 , 1) } is a basis for R 3 . b) If [ ±v ] B = 1 2 3 , what is ±v ? c) Determine the coordinates of ±x = (1 , 1 , 1) and ± y = (4 , - 2 , 7) with respect to B . 2: Find a basis and determine the dimension of S = span { x 2 +2 x +1 , 2 x 2 +3 x - 2 , - x 2 +7 , 2 x 2 +2 x +1 } . 3: Find a basis of M
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Unformatted text preview: (2 , 2) that includes 1 2 3 4 , 4 3 2 1 . 4: Let V be a vector space with basis B = { v 1 , . . . ,v n } and let x, y V and a, b R . Prove that [ ax + by ] B = a [ x ] B + b [ y ] B . 1...
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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