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e507k - MAS 3105 Quiz 5 Key Prof S Hudson 1 Find the matrix...

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MAS 3105 March 15, 2007 Quiz 5 Key Prof. S. Hudson 1) Find the matrix representation A of the linear operator L : R 2 R 2 that reflects each vector x about the line x 2 = x 1 and then projects it onto the x 1 -axis. 2) Answer TRUE or FALSE: Part a) refers to the ‘baby rabbit example’ from the lectures. a) With 2 adults and 3 baby rabbits this year, we’ll have 9 rabbits total, next year. b) The commuting diagram for Ch 4.3 (similarity) contains only one vector space, V . c) If A is similar to itself, then A is nonsingular. d) If A and B are row equivalent they have the same column space. e) The matrix A that answers problem 1) has rank = 1. 3) Choose ONE of these. a) Suppose A and B are nxn and B is nonsingular. Prove that rank ( BA ) = rank ( A ). [Hint: compare their nullspaces] 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) State the formula in Thm 5.1.1 for x T y and prove it (in R 2 ). Remarks and Answers: The average was about 40/60. The unofficial scale is: A’s 45-60, with 6 points per letter below that. I computed your semester average, based on
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