2025A2 - multiplication by numbers). (5 pts) 2. Describe...

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MATH 2025 Spring 2007 Assignment 2 Due Monday, March 5, 2007 before the class 1. Determine if the sets of vectors are linearly independent. If, for any of these, the answer can be determined by inspection (i.e., without calculation), state why. For any sets that are linearly dependent, find a dependence rela- tionship among the vectors. a) (0 , 0 , 0 , 1) , (0 , 0 , 2 , 1) , (0 , 3 , 2 , 1) , (4 , 3 , 2 , 1) in R 4 (5 pts) b) χ [0 , 2 / 3) , χ [2 / 3 , 1) , χ [0 , 1) in PC [0,1] (5 pts) c) ± 1 1 0 2 ² , ± 0 0 0 1 ² , ± 0 2 0 0 ² , ± 2 0 0 0 ² in the vector space of all 2 × 2 real matrices (with usual matrix addition and
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Unformatted text preview: multiplication by numbers). (5 pts) 2. Describe the span of the vectors (0 , 0) , (3 , 4) in R 2 a) geometrically [what geometric object it is] (5 pts) b) algebraically [equation] (5 pts) 3. Determine the constants a, b, c R such that a) (4 ,-1 , 2) = a (1 , 2 , 0) + b (1 , 1 , 1) + c (1 , , 1) (5 pts) b) (2 ,-4 , 3) = a (1 ,-1 , 1) + b (1 , 1 , 0) + c (1 ,-1 ,-2) (5 pts)...
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