tut1 - 4: For each of the following sets, determine if the...

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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.
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Unformatted text preview: 4: For each of the following sets, determine if the set is linear independent and describe 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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