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Unformatted text preview: independence. ..) Check the class FAQ for some more information on a few of these topics. Now, for a few sample problems: • Find the LU decomposition of M = 1 2 3 4 5 6 3 2 1 . Use the LU decomposition to solve the system MX = V , where V = 3 4 5 . • Suppose I use row operations to transform M = 1 2 31 23 3 2 1 into M = 9 6 3 0 4 0 1 2 3 . Find a matrix E such that EM = M . • Prove that if RREF ( M ) = 1 2 3 4 5 6 0 0 0 , then M cannot have an inverse. • What is the determinant of the inverse of the transpose of M = 1 03 2 0 01 8 3 1 0 21 0 ? 1 • Is 1 2 3 in the span of S = { 3 2 1 , 4 2 3 , 2 8 8 } ? Are the vectors in S linearly independent? Prove or disprove. 2...
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 Spring '10
 Pon
 Linear Algebra, Invertible matrix

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