M235A5 - MATH 235 Orthogonality & Gram-Schmidt...

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Unformatted text preview: MATH 235 Orthogonality & Gram-Schmidt Assignment 5 Hand in questions 3,9,11,13,14 by 9:30 am on Wednesday November 1, 2006. 1. Determine which pairs of vectors are orthogonal. Find norm of each vector (a) u = i 2 1 , v = i 2- 1 b) u = 1 / 2 1 / 2 1 / 2 1 / 2 , v = 1 / 2- 2 2. Let u 1 = (3 , , 1) T , u 2 = (0 , 1 , 0) T , and y = (0 , 3 , 10) T . Let W = Span(u 1 , u 2 ). Repre- sent y as the sum of a vector in W and a vector in orthogonal complement of W . 3. Let V be the null space of A where A = 1- 1- 3 2 1 2- 1 4 2 1 3 4 3 2 1 5 6 and let v = 5 1 3- 2 1 . (a) Find a basis for V . (b) Find the distance from v to V . 4. Find an orthogonal basis for the span of X 1 = (1 , 1 , , 1), X 2 = (0 , 1 ,- 1 , 1) and X 3 = (1 , , 1 , 1). 5. Find an orthogonal basis for the column space of A = 1 1 0- 1 0 1 1 1 0 1 ....
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M235A5 - MATH 235 Orthogonality & Gram-Schmidt...

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