tut1 - the span of the set. a) { (2 ,-1 , 2) , (3 , 1 , 1)...

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Math 136 Tutorial 1 Problems 1: Let ~x = (3 , 5 , - 1) and ~ y = (2 , - 1 , 1). Calculate 2 ~x - 3 ~ y , ( ~x + ~ y ) · ~x and determine if ~x and ~ y are orthogonal. 2: Verify the Cauchy-Schwarz inequality and the triangle inequality if ~x = (2 , - 6 , - 3) and ~ y = ( - 3 , 4 , 5). 3: Find an equation for the plane through (1 , - 3 , - 1) that is parallel to the plane 2 x 1 - 3 x 2 + 5 x 3 = 17. 4: For each of the following sets, determine if the set is linear independent and describe
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Unformatted text preview: the span of the set. a) { (2 ,-1 , 2) , (3 , 1 , 1) , (-4 , 2 ,-4) } . b) { (1 , 2 , 0) , (0 , , 0) } . c) { (1 , , 1 , 3) , (2 , , , 1) , (-3 , 2 ,-1 , 1) } . 1...
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This note was uploaded on 01/06/2011 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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