Test2(sol) - J: \ - L u T t t " f rl': .! NC State...

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.! J: \- L u Tt t" frl': MA 405. Linear Algebra I Dr. Alina Duca NC State University Mathematics Department Test 2 March 18,2009 NAME (please print legibty): INSTRUCTIONS: This is a 50 minutes exam. Show your work and justify your steps for full credit. Partial credit will be given for correct work neatly presented. No texts, notes, or other aids are permitted. Calculators are NOII pennitted. Please turn off your cellphones. Please check that you have all 5 pages. Please be careful not to loosen the staple. The value of each question is indicated in the lefthand 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. Question Points Score 1 12 2 I2 a J 10 4 5 6 Total: 50 EXAM QUESTIONS: [l2] 1. Answer only 3 out of 5. Please circle which parts you vrish to be graded. (a) If A is a 5 x 5 matrix and NS(A) is the zero subspace, what can you say about solutions of linear systerns Ax-bforbelRs. Nbf A\ *io J *> *he hou' ".J" *o Glr/.s si1 s{e-rl-, * X ="3 "=') cLL{ k "*.o L^*r:rX, L"r *r.h;* '-. .'l :*{ -) AtU sy.rkre-r prE=T hos L'L'n5:14-2;''/*-d'e* ' (b) Construct a 3 x 4 matrix A such that dim(NS(A)) : 2 and dim(Cs(, )) 2. r/':\ , '\ \ . L-> raraLA --- 2- lu) ? 5 -1 I 'i1{.*nnors. lo ,.D a trl Lo o oJ (c) Let M be ay'3 x 3 invertible matrix. Explain why the row space and the column space of M are equal to R3.
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This note was uploaded on 06/11/2010 for the course MA 405 taught by Professor Staff during the Spring '08 term at N.C. State.

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Test2(sol) - J: \ - L u T t t " f rl': .! NC State...

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