practice-Math33A-final

# practice-Math33A-final - Name: Student ID: Section: 2 Prof....

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Name: Student ID: Section: 2 Prof. Alan J. Laub June 9, 2008 Math 33A – FINAL EXAMINATION Spring 2008 Instructions: (a) The exam is closed-book (except for one page of notes) and will last two and a half (2.5) hours. (b) Notation will conform as closely as possible to the standard notation used in the lectures. (c) Do all 6 problems. Problems 1–5 are worth 15 points each; problem 6 is worth 25 points (5 subparts, each worth 5 points). Some partial credit may be assigned if warranted. (d) Label clearly the problem number and the material you wish to be graded. 1. Consider the initial-value problem ˙ x ( t ) = Ax ( t ); x (0) = x 0 for t 0. Let A = - 7 5 - 10 8 and x 0 = 1 0 . Determine an explicit expression for x ( t ), i.e., solve the initial value problem.

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2. Let A IR m × n and deﬁne the three matrices B k = I - kAA + for k = 1 , 2 , 3. (a) Which of B 1 ,B 2 ,B 3 are symmetric? (b) Which of
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## This note was uploaded on 05/29/2011 for the course MATH 33a taught by Professor Lee during the Spring '08 term at UCLA.

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practice-Math33A-final - Name: Student ID: Section: 2 Prof....

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