exam_1_20F_solutions

exam_1_20F_solutions - Name Student ID TA/Section(circle...

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Unformatted text preview: Name Student ID TA/Section (circle): Katie 12pm-C01 1pm-C02 2pm-C03 Mary 3pm-C04 8pm-C05 9pm-C06 Math 20F, Winter 2010, Midterm Exam 1 Solutions • Show all of your work and justify your answers to receive full credit. • Write your answers and work clearly and legibly; no credit will be given for illegible solutions. • Go back and check your answers if you finish early. # Points Score 1 6 2 3 3 2 4 3 5 2 6 2 7 2 Σ 20 1. Let A = 1 1 1 2 3 1 − 1 − 2 and b = 4 7 − 5 (a) (4 points) Find the solution set of the equation A x = b . Write your answer in parametric vector form . Answer: We row reduce the augmented matrix. 1 1 1 4 2 3 1 7 − 1 − 2 − 5 ∼ 1 1 1 4 1 − 1 − 1 1 − 1 − 1 ∼ 1 1 1 4 1 − 1 − 1 ∼ 1 2 5 1 − 1 − 1 Column three is not a pivot column, so x 3 is a free variable. This gives the equations x 1 + 2 x 3 = 5 x 2 − x 3 = − 1 or rearranging, x 1 = 5 − 2 x 3 x 2 = − 1 + x 3 In parametric vector form this is x = x 1 x 2 x 3 = 5 − 2 x 3 − 1 + x 3 x 3 = 5 − 1 + x 3 − 2 1 1 (b) (2 points) What is the parametric vector form of the solution set of the system A x = ?...
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This note was uploaded on 03/17/2011 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

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exam_1_20F_solutions - Name Student ID TA/Section(circle...

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