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Unformatted text preview: L : V W be a linear mapping. Prove that if { L ( ~v 1 ) ,...,L ( ~v k ) } is a linearly independent set in W , then { ~v 1 ,...,~v k } is a linearly independent set in V . (b) Give an example of a linear mapping L : V W where { ~v 1 ,...,~v k } is linearly independent in V , but { L ( ~v 1 ) ,...,L ( ~v k ) } is linearly dependent in W . 7. Let U , V be nite dimensional vector spaces and let L : V U be a linear mapping and M : U U be a linear operator such that Ker( M ) = { ~ } . Prove that rank( M L ) = rank( L )....
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 Spring '08
 CELMIN
 Math

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