Linear Algebra Solutions 5

Linear Algebra Solutions 5 - 14. Suppose that (1 , . . . ,...

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14. Suppose that ( α 1 ,...,α n ) and ( β 1 ,...,β n ) are solutions of the system of linear equations n X j =1 a ij x j = b i , 1 i m. Then n X j =1 a ij α j = b i and n X j =1 a ij β j = b i for 1 i m . Let γ i = (1 - t ) α i + i for 1 i m . Then ( γ 1 ,...,γ n ) is a solution of the given system. For n X j =1 a ij γ j = n X j =1 a ij { (1 - t ) α j + j } = n X j =1 a ij (1 - t ) α j + n X j =1 a ij j = (1 - t ) b i + tb i = b i . 15. Suppose that ( α 1 ,...,α n ) is a solution of the system of linear equations n X j =1 a ij x j = b i , 1 i m. (1) Then the system can be rewritten as n X j =1 a ij x j = n X j =1
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This note was uploaded on 12/19/2011 for the course MAS 3105 taught by Professor Dreibelbis during the Fall '10 term at UNF.

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