Exam2A - M340L EXAM 2A SPRING 2010 Dr Schurle Your name...

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M340L EXAM 2A Your name: SPRING, 2010 Dr. Schurle 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 . The vector space V may not be any R q , so you CANNOT use columns or matrices or pivots in your explanation. 2. (10 points) Suppose H is a n × n matrix and the equation H x = c is inconsistent for some c in R n . Does the equation H x = 0 have a nontrivial solution? Justify your answer.
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YOUR SCORE: /100 3. (10 points) Suppose that A is a p × q matrix. Explain in detail why rank A + dim Nul A = q . 4. (10 points) Let H be the set of all vectors in R 3 lying on or above the xy -plane, that is, H is the set of all x y z such that z 0. Is H a subspace of R 3 ? Justify your answer.
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5. (12 points) The matrix A =
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