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MA405,T1,Solutions - NC State Universify Mathematics...

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NC State Universify Mathematics Deparfment MA 405. Linear Algebra I Dr. Alina Duca Test 1 February 11,2009 5cL UT1t)5i5 NAME (please print legibly): INSTRUCTIONS: This is a 50 minutes exam. Show your work and justify your steps for fuIl credit. Partial credit will be given for correct work neatly presented. No texts, notes, or other aids are permitted. Calculators are NOT permitted. Please rurn off your cellphones. Please check that you have all 6 pages. Please be careful not to loosen the staple. The value of each question is indicated in the lefthand margin beside the statement ofthe question. The total value ofall questions is 50. Answer all questions on the exam paper in the space provided beneath the ques- tion. If you need more room, I will provide you with more paper where you may continue your work, but clearly indicate that your work is continued. Question Points Score 8 2 6 3 10 4 10 5 10 6 6 Total: 50 EXAM QUESTIONS: t8l 1. In each question circle either TRUE of FALSE. No justification is needed. Answer only 4 out of 6. Please circle which parts you wish to be graded. (a) If A is a 4 x 4 matrix, then det(4A) : qde(A). - TRTIE FALSE \ (b) If ,4 and B are nx nmaftices,with detA:2 arlddett 3,thendet A+ B:5. TRUE FALSE ) (c) Ra is a subspace of iR5. TRUE FALSE .] (d) If a linear system has twq different solufions, it must have infinitely many solutions.
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