quiz 5 answers

Linear Algebra with Applications

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Name: Tuesday section time: Student ID: Math 20F - Linear Algebra - Winter 2003 Quiz #5 — February 18 (Do not discuss the quiz with students who haven’t taken it yet – until 8:00pm.) (Do not calculate more than is necessary to answer a problem! For one of these problems the answer(s) should be obvious from inspection.) 1. Let v 1 =(1 , - 1) T and v 2 , 2) T ,so v 1 , v 2 are a basis for R 2 . Let x =(3 , 2) T . What are the coordinates x with respect to the basis v 1 , v 2 ? METHOD: You need to find a 1 ,a 2 so that x 1 = a 1 v 1 + a 2 v 2 . For this you solve the matrix equation ± 11 - 12 ¶± a 1 a 2 = ± 3 2 . This can be done either by row operations, or by inverting the 2 × 2 matrix. ANSWER: The coordinates of x w.r.t. the basis v 1 , v 2 are ( 4 3 , 5 3 ) . That is, x = 4 3 v 1 + 5 3 v 2 . 2. Let
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This homework help was uploaded on 01/23/2008 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

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