Unformatted text preview: M ◦ L ) ≤ rank( M ). b) Prove that rank( M ◦ L ) ≤ rank( L ). c) Prove that if M is invertible, then rank( M ◦ L ) = rank L . 3. Let T : V → W be a linear mapping and let { ~v 1 ,...,~v r ,~v r +1 ,...,~v n } be a basis for V such that { ~v r +1 ,...,~v n } is a basis for Null( T ). Prove that { T ( ~v 1 ) ,...,T ( ~v r ) } is a basis for the range of T ....
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 Spring '10
 WILKIE
 Math, Linear Algebra, Rank, basis, rank L.

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