Quiz7-Solutions

Quiz7-Solutions - Name:. Math 331 - Quiz 7 - Solutions...

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Name:. ......................................................................................... Math 331 - Quiz 7 - Solutions Thursday, October 27 1. Find an LU -factorization of ± 2 5 - 3 - 4 ² Solution: Row reduce the matrix to echelon form. ± 2 5 - 3 - 4 ² II + 3 2 I ----→ ± 2 5 0 7 2 ² Then U = ± 2 5 0 7 2 ² and L = ± 1 0 - 3 2 1 ² . Check: LU = ± 1 0 - 3 2 1 ²± 2 5 0 7 2 ² = ± 2 5 - 3 - 4 ² 2. Let A = 1 3 2 - 6 3 9 1 5 2 6 - 1 9 5 15 0 14 The echelon form of A is A = 1 3 3 2 0 0 5 - 7 0 0 0 5 0 0 0 0 Use this information to find a basis for Col( A ). What is the dimension of Nul( A )? Justify your answer. Solution: The pivot columns of A always form a basis for Col( A ). From the echelon form of
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