Exam2A - M340L EXAM 2A SPRING, 2009 Dr. Schurle Your name:...

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M340L EXAM 2A 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 inside 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.
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4. (12 points) The matrix A = 1 2 2 1 15 - 1 0 0 2 2 20 4 1 2 5 3 37 - 2 3 6 1 1 19 - 2 - 2 - 4 - 3 1 - 4 0 is row equivalent to the matrix B = 1 2 0 0 3 0 0 0 1 0 2 0
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Exam2A - M340L EXAM 2A SPRING, 2009 Dr. Schurle Your name:...

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