Name:Tuesday section time:Student ID:Math 20F - Linear Algebra - Winter 2003Quiz #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 ofthese problems the answer(s) should be obvious from inspection.)1. Letv1=(1,-1)Tandv2,2)T,sov1,v2are a basis forR2.Letx=(3,2)T.What are the coordinatesxwith respect to the basisv1,v2?METHOD: You need to ﬁnda1,a2so thatx1=a1v1+a2v2. For thisyou solve the matrix equation±11-12¶±a1a2¶=±32¶. This canbe done either by row operations, or by inverting the2×2matrix.ANSWER: The coordinates ofxw.r.t. the basisv1,v2are(43,53). Thatis,x=43v1+53v2.2. 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.