2025A2_6S

2025A2_6S - determine the constants a,b,c R such that (4...

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MATH 2025 Spring 2006 Assignment 2 Due Monday, March 6, 2006 before the class Please show all work! 1. Determine if the following set of vectors is linearly independent or not. If the vectors are linearly dependent write one of them as a combination of the others: a) (1 , 1 , - 1 , 1) , (1 , 2 , 3 , 2) , (1 , - 2 , 2 , 0); (5 pts) b) (1 , 1 , 2) , (1 , 1 / 3 , 0) , ( - 1 , 0 , 1). (5 pts) 2. Show that the vectors (1 , - 1 , 1) , (1 , 1 , 0) , (1 , - 1 , - 2) form an orthogonal basis for R 3 and determine the constants a,b,c R such that (2 , - 4 , 3) = a (1 , - 1 , 1) + b (1 , 1 , 0) + c (1 , - 1 , - 2) . (5 pts) 3. Show that the vectors (1 , 2 , 0) , (1 , 1 , 1) , (1 , 0 , 1) form a basis for R 3 . Then
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Unformatted text preview: determine the constants a,b,c R such that (4 ,-1 , 2) = a (1 , 2 , 0) + b (1 , 1 , 1) + c (1 , , 1) . (5 pts) 4. Describe the span of the vectors (1 , ,-1) , (-1 , 1 , 0) , (0 ,-1 , 1) a) algebraically; (5 pts) b) geometrically. (5 pts) 5. Starting from the set of vectors (1 , 1 , 0) , (0 , 1 , 1) , (1 , , 1) use the Gram-Schmidt orthogonalization to construct a set of orthogonal vectors with the same linear span. (5 pts)...
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