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Unformatted text preview: 11 and whose range is Span 3 5 . 6. Let { ~v 1 ,...,~v k } be a set in R n such that Span { ~v 1 ,...,~v k } = R n . Let L : R n R m be a linear mapping such that Range( L ) = R m . Prove that Span { L ( ~v 1 ) ,...,L ( ~v k ) } = R m . 7. Let T : R n R m be a linear mapping. Suppose that { ~v 1 ,...,~v k } a linearly dependent set in R n . Prove that { T ( ~v 1 ) ,...,T ( ~v k ) } is a linearly dependent set in R m . 1...
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 Winter '08
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 Math, Matrices

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