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02spr-m2 - EXAM II Math 51 Spring 2002 You have 2 hours No...

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EXAM II Math 51, Spring 2002. You have 2 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number 1. (/30 points) 2. (/30 points) 3. (/30 points) 4. (/30 points) 5. (/30 points) Bonus (/15 points) Total (/150 points) “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: Circle your TA’s name: Tarn Adams (2 and 6) Mariel Saez (3 and 7) Yevgeniy Kovchegov (4 and 8) Heaseung Kwon (A02) Alex Meadows (A03) Circle your section meeting time: 11:00am 1:15pm 7pm 1
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1. (a) Without computing the inverse directly, explain how you know that the matrix A given below is invertible. A = 3 0 2 0 2 4 0 0 1 (b) Find A - 1 . 2
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2. For each of the following, either (i) find a matrix (or matrices) satisfying the given de- scriptions, or (ii) prove that such a matrix (or matrices) cannot exist.
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