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MA405Test3(sol)

MA405Test3(sol) - NC StateUniversity Mathematics eparhnent...

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NC State University Mathematics Deparhnent Test 3 April t5,2009 NAME (ptease print tegibty): o t".l 3 INSTRUCTIONS: This is a 50 mlnutes exam. Show your work and justify your steps for full credit. Partial credit will be grven for correct work neafly presented. No texts, notes, or other aids are perrritfed. Calculators are NCrf permitted. please turn off your cellphones. Please check that you have all 6 pages. Pleasebe careful not to loosen the staple. The value of each question is indicated in the lefttrand margin beside the statement of the question. The total value of all questions is 50. Answer all questions on the exam paper in the space provided beneath the question. MA 405. Linear Algebra I Dr. Alina Duca Question Points Score I 6 2 12 3 10 4 12 5 10 Total: 50 EXAM QTTESTTONS: 161 1. Prove that if vlr . . . ,yn -!n ct j\ f,V, 4 -i Fo r elr4 i :,- l (J) /T, A ) 3'"/' 't :- -)' C, { q ,V, )+ (*',/*:: # . ,r\A , b4 "l rr\J .{ c4^l/*, > r* +- C, < t/,' -A-l L ) are orthogonal vectors in an inner product space V, then they are linearly independent. o kt'rrn u () 1t; - Va-, > -1 fi I I \ t:, I Thu-{ 1( €; lt\/d ll J, {(a , V; '7 -r' Ci* f U; ,O;* l* , + 4M{TL.

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MA405Test3(sol) - NC StateUniversity Mathematics eparhnent...

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