33asamplemidterm1winter2009

# 33asamplemidterm1winter2009 - . ANSWER: (b) Solve 1 2 3 1 2...

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Maths 33a - Sample Midterm 1 Instructor : R. N. Fernandez Name (please print legibly): Student ID Number: Section Number: Signature: Jennifer Padilla (2a, Tues.) Jennifer Padilla (2b, Thurs.) Jack Buttcane (2c, Tues.) Jack Buttcane (2d, Thurs.) There are ﬁve questions on this examination. Do not turn this page until told that you may do so by a proctor. Calcula- tors, notes and books may not be used in this examination. You may not receive full credit for a correct answer if insuﬃcient work is shown. Where applicable, put ﬁnal answers in the spaces provided. Please indicate clearly if you are using the backs of pages. You may use blank sheets at the end of this booklet. Part A QUESTION VALUE SCORE 1 10 2 10 3 10 4 10 5 10 TOTAL 50 1

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Part A 1. (10 points) (a) Calculate the rank of 1 2 3 1 1 1 5 7 9 . ANSWER: (b) Does 1 2 3 1 1 1 5 7 9 x y z = 1 1 5 have a unique solution? You must justify your answer. ANSWER: 2
2. (10 points) (a) Calculate the inverse of 1 2 3 1 2 1 1 0 1

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Unformatted text preview: . ANSWER: (b) Solve 1 2 3 1 2 1 1 0 1 x y z = 1 1 1 . ANSWER: 3 3. (10 points) Determine whether the following system of equations is consistent (i.e. has at least one solution). If it is, nd the solution(s). x + y + z = 2 x + y + 2 z = 2 2 x + 2 y + 3 z = 4 . ANSWER: 4 4. (10 points) (a) Let T : R 2 R 2 be the linear transformation that projects onto the x-axis (i.e. T ( x ) = proj L ( x ), where L is the x-axis). Determine the matrix of T (and justify your answer). ANSWER: 5 (b) Let S : R 2 R 2 be the linear transformation that reects through the x-axis. Let W ( x ) = S ( S ( x )). Determine the matrix of W . 6 5. (10 points) Suppose that the 4 2 matrix A satises A-1 ! = 1 1 . and A 1 1 ! = 1 1 1 . Calculate the matrix of A . ANSWER: 7 8...
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## This note was uploaded on 04/26/2009 for the course MATH 33a taught by Professor Lee during the Winter '08 term at UCLA.

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33asamplemidterm1winter2009 - . ANSWER: (b) Solve 1 2 3 1 2...

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