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Test2(sol)

# Test2(sol) - J L u T t t f rl NC State University...

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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. Pleasecheck 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 beneaththe question. Question Points Score 1 12 2 I2 a J 10 4 10 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.

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Test2(sol) - J L u T t t f rl NC State University...

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