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**Unformatted text preview: **MATH 51 MIDTERM I October 19, 2006 Instructions: No calculators, books, notes, or electronic devices may be used during the exam. You have 90 minutes. There are 7 problems, each with multiple parts. You should work quickly so as to not leave out problems towards the end of the exam. Write solutions 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 (15 points) Problem 2 (15 points) Problem 3 (20 points) Problem 4 (15 points) Problem 5 (15 points) Problem 6 (10 points) Problem 7 (10 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) 1. (a) Find the reduced echelon form of 1 0 1- 1 0 0 1 2- 3 0 0 1 2 3 1 0 1 2 3 . (b) Consider the matrix A = 1 1 1 1 2 a 1 3 b where a and b are real numbers. Show that the null space of A is either { }...

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