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Unformatted text preview: the system has a unique solution. What does the reducedrow echelon form of the coeﬃcient matrix of this system look like ? Use ﬂ to denote a pivot and * to denote an entry that may or may not be zero. 4. Identify precisely all conditions on a,b,c,d under which the columns of A = a a a a a b b b a b c c a b c d are linearly independent. Before you begin, explain your approach in a brief sentence. 5. If the vectors u , v and w of a vector space V are linearly independent, does it necessarily follow that the vectors u + v , v + w and w + u will always be linearly independent ? 1 6. Does the vector x = 113 belong to the subspace of 3dimensional space < 3 spanned by the vectors a = 1 1 2 and b = 2 1 4 ? 2...
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 Fall '07
 UNKNOWN
 Linear Algebra, Linear Equations, Vector Space, rowreduced echelon matrices

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