07win-f

07win-f - Math 51 Winter 2007 Final Exam FINAL EXAM This is...

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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
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 FINAL EXAM This is...

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