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Exam2B200

# Exam2B200 - M340L EXAM 2B 2:00 FALL 2009 Dr Schurle Your...

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M340L EXAM 2B 2:00 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 V is a vector space with a basis consisting of exactly n vectors. Explain in detail why any set of more than n vectors in V must be linearly dependent. The vector space V need not be any R q .

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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 . Is H a subspace of R 3 ? Justify your answer. 3. (12 points) Suppose the rank of a 23 × 17 matrix A is 15. The largest number of linearly independent vectors in Row A is . The smallest number of vectors needed to span Col A is . The null space of A is a subspace of R q when q = . How many vectors are in a basis for Nul A ?
4. (12 points) The matrix A = 2 1 14 0 3 40 1 1 11 4 - 2 23 0 - 2 - 16 4 - 4 - 16 - 2 1 2 0 4 28 1 - 2 - 13 0 7 49 is row equivalent to the matrix B =

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Exam2B200 - M340L EXAM 2B 2:00 FALL 2009 Dr Schurle Your...

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