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# Exam2B - M340L EXAM 2B SPRING 2009 Dr Schurle Your name...

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M340L EXAM 2B SPRING, 2009 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (10 points) Suppose that v 1 , v 2 , . . . , v p are vectors in a vector space V and that H = Span { v 1 , v 2 , . . . , v p } . Explain in detail how to get a basis for H that consists of vectors from the list v 1 , v 2 , . . . , v p .

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YOUR SCORE: /100 2. (10 points) Let H be the set of points outside and on the unit circle in R 2 , that is, H is the set of all " x y # such that x 2 + y 2 1. Is H a subspace of R 2 ? Justify your answer. 3. (10 points) Suppose A is a p × q matrix. Explain in detail why rank A +dim Nul A = q.
4. (12 points) The matrix A = 1 2 9 1 - 1 7 0 2 4 2 4 42 1 5 15 3 - 2 12 3 1 17 1 - 2 10 - 2 - 3 - 16 1 0 - 21 is row equivalent to the matrix B = 1 0 5 0 0 7 0 1 2 0 0 3 0 0 0 1 0 2 0 0 0 0 1 8 0 0 0 0 0 0 .

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