A1 - ~v 1,~v r,~v r 1,~v n be a basis for V such that ~v r...

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Math 235 Assignment 1 Due: Wednesday, May 12th 1. Let A be an m × n matrix and B be an n × p matrix. a) Prove that rank( AB ) rank( A ). b) Prove that rank( AB ) rank( B ). c) Prove that if B is invertible, then rank( AB ) = rank( A ). 2. Let T : V W be a linear mapping and let
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Unformatted text preview: { ~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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