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Unformatted text preview: Math 136 Assignment 4 Solutions 1. Let B = 1 1 1 , 2 2 , 2 1 1 . Determine if ~v = 6 3 is in the span of B . Solution: We want to determine if there are constants t 1 ,t 2 ,t 3 such that 6 3 = t 1 1 1 1 + t 2 2 2 + t 3 2 1 1 = t 1 + 2 t 2 t 1 + 2 t 3 t 3 t 1 + 2 t 2 + t 3 We row reduce the augmented matrix of the corresponding system to get 1 2 6 1 0 2 0 0 1 1 2 1 3 1 0 0 0 1 0 0 0 1 0 0 0 1 Hence, the system is inconsistent, so the vector is not in the span. 2. Determine whether the set 1 1 1 , 1 2 1 , 1 1 2 2 , 1 3 1 1 is linearly independent. If the set is linearly dependent, find all linear combinations of the vectors that are ~ 0....
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 Winter '08
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 Math

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