06aut-m2

# 06aut-m2 - MATH 51 Instructions MIDTERM II No calculators...

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MATH 51 MIDTERM II November 16, 2006 Instructions: No calculators, books, notes, or electronic devices may be used during the exam. You have 90 minutes. There are 9 problems, many with multiple parts. Many questions have short answers requiring no computation. The point value of each part of each problem is indicated in brackets at the beginning of that part. You should work quickly so as to not leave out problems towards the end of the exam. Show computations on the exam sheet. If extra space is needed use the back of a page. Name: (print clearly) Signature: (for acceptance of honor code) Problem 1 (10 points) Problem 2 (10 points) Problem 3 (12 points) Problem 4 (10 points) Problem 5 (12 points) Problem 6 (13 points) Problem 7 (13 points) Problem 8 (15 points) Problem 9 (5 points) Total (100 points) Your TA/discussion section (circle one): Antebi (15, 18) Ayala (3, 6) Easton (14, 17) Fernanadez (2, 5) Kim (8, 11) Koytcheﬀ (9, 12) Lo (21, 24) Rosales (26, 27) Tzeng (20, 23) Zamﬁr (29, 30) Schultz (51A)

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1. (a) [2] If A is an m × n matrix ( m rows, n columns) so that the transformation T ( x ) = A x is one-to-one, what is rank( A )? (Circle one.)
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06aut-m2 - MATH 51 Instructions MIDTERM II No calculators...

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