Unformatted text preview: S . We have to prove that X 1 , X 1 + X 2 ,...,X 1 + Â·Â·Â· + 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 ) + Â·Â·Â· + x m ( X 1 + Â·Â·Â· + X m ) = 0 . Then ( x 1 + x 2 + Â·Â·Â· + x m ) X 1 + Â·Â·Â· + x m X m = 0 . Then the linear independence of X 1 ,...,X m gives x 1 + x 2 + Â·Â·Â· + x m = 0 ,...,x m = 0 , 35...
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 Fall '10
 Dreibelbis
 Linear Algebra, Linear Independence, Following, basis, All wheel drive vehicles

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