# Linear Algebra with Applications

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• davidvictor
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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 = (1 , 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 1 1 - 1 2 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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