Unformatted text preview: b) Suppose that L : V → W is linear and S is a subspace of V . Prove that L ( S ) is a subspace of W . c) The dimension of Col(A) equals the dimension of Row(A). Answers: 1) TTTFT 2) This was a HW problem. Set S = U1 V (maybe from an arrow diagram), which is easiest to get from [ U  V ] → [ I  S ]. S = 112 1 1 1 1 3) These proofs are in the textbook [though I think my proof of c) is clearer than the book’s]. 1...
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Matrices, Row, row space, singular matrix, Prof. S. Hudson

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