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Exam2B900

# Exam2B900 - M340L EXAM 2B 9:00 FALL 2009 Dr Schurle Your...

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M340L EXAM 2B 9:00 FALL, 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 3 are vectors in a vector space V . Explain in detail why Span { v 1 , v 2 , v 3 } is a subspace of V .

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YOUR SCORE: /100 2. (10 points) Let H be the set of all x y z such that z = x + y + 2. Is H a subspace of R 3 ? Justify your answer. 3. (12 points) Suppose the rank of a 19 × 15 matrix A is 12. The smallest number of vectors needed to span Col A is . The largest number of linearly independent vectors in Nul A is . The row space of A is a subspace of R q when q = . Does A x = b have a solution for every b in R 15 , yes or no?
4. (12 points) The matrix A = 2 6 10 1 8 0 1 3 5 1 6 4 0 0 0 - 2 - 8 4 - 2 - 6 - 10 1 0 0 1 3 5 - 2 - 6 0 is row equivalent to the

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Exam2B900 - M340L EXAM 2B 9:00 FALL 2009 Dr Schurle Your...

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