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Unformatted text preview: S . We have to prove that X 1 , X 1 + X 2 ,...,X 1 + + X m also form a basis for S . First we prove the independence of the family: Suppose x 1 X 1 + x 2 ( X 1 + X 2 ) + + x m ( X 1 + + X m ) = 0 . Then ( x 1 + x 2 + + x m ) X 1 + + x m X m = 0 . Then the linear independence of X 1 ,...,X m gives x 1 + x 2 + + x m = 0 ,...,x m = 0 , 35...
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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.
 Fall '10
 Dreibelbis

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