07win-f - Math 51, Winter 2007 Final Exam March 19, 2007...

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Math 51, Winter 2007 Final Exam March 19, 2007 FINAL EXAM This is a closed-book, closed-notes exam. No calculators or other electronic aids will be permitted. In order to receive full credit, please show all of your work and justify your answers. You do not need to simplify your answers unless specifically instructed to do so. Please sign the following: “On my honor, I have neither given nor received any aid on this examina- tion. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Name: Signature: 1 10 pts 9 8 pts 2 8 pts 10 5 pts 3 5 pts 11 5 pts 4 7 pts 12 12 pts 5 10 pts 13 10 pts 6 17 pts 14 10 pts 7 10 pts 15 10 pts 8 15 pts Total 142 pts Circle your TA’s name Lan Oren Josh Peter Chad Leo Rob Nikola Jian Page 1 of 16
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Math 51, Winter 2007 Final Exam March 19, 2007 (1) (10 points) Find bases of the null space and the column space of the matrix A = 1 2 0 1 2 1 2 0 2 3 1 2 0 3 4 1 2 0 4 5 . Page 2 of 16
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Math 51, Winter 2007 Final Exam March 19, 2007 (2) (8 points) What condition(s) must b 1 , b 2 , b 3 and b 4 satisfy so that the following system has a solution? x - 3 y = b 1 3 x + y = b 2 x + 7 y = b 3 2 x + 4 y = b 4 Page 3 of 16
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Math 51, Winter 2007 Final Exam March 19, 2007 (3) (5 points) Let -→ x , -→ y , and -→ z be vectors in R n whose magnitudes are 1 , 2, and 3 respectively. Suppose that -→ x is parallel to (and in the same direction as) -→ y , and -→ x is perpendicular to
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07win-f - Math 51, Winter 2007 Final Exam March 19, 2007...

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