240S10Final

# 240S10Final - 1 Math 240 Circle one FINAL EXAM May 4 2010...

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1 Math 240 FINAL EXAM May 4, 2010 Circle one: Professor Ziller Professor Zywina Name: Penn Id#: Signature: TA: Recitation Day and Time: You need to show your work, even for multiple choice problems. A correct answer with no work will get 0 points. The only exception are True/False problems, where no work needs to be shown. Each problem is worth 10 points. You are NOT allowed to use a calculator. The extra double sided sheet of paper needs to be hand written in your own hand writing (no copies allowed). (Do not ﬁll these in; they are for grading purposes only.) 1) 9) 2) 10) 3) 11) 4) 12) 5) 13) 6) 14) 7) 15) 8) Total

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Math 240 FINAL EXAM May 4, 2010 Name: 2 1. For what values of a does the following system have inﬁnitely many solutions? x + y + z = 1 2 x + ay + z = 0 - x + y + z = 3 Answer: (a) 0 (b) 3 (c) 2 (d) 1 (e) 4 (f) - 8
Math 240 FINAL EXAM May 4, 2010 Name: 3 2. (a) Find the rank of the matrix A = 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 (b) What is det A ? (c) The set of solutions of the homogeneous system AX = 0 depends on how many arbitrary parameters?

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Math 240 FINAL EXAM
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240S10Final - 1 Math 240 Circle one FINAL EXAM May 4 2010...

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