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MA222FINAL2010

# MA222FINAL2010 - COURSE MA 222 LINEAR ALGEBRA INSTRUCTOR...

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COURSE: MA 222 LINEAR ALGEBRA INSTRUCTOR: AYHAN SEV İ M DATE: May 21, 2010 TIME: 10:00-11:30 (90 Minutes) The number of points for each problem is given in the brackets. Show all your work. Correct answers without sufficient explanation might not get full credit. Calculators are not allowed. Final exam affects 60% on grading. FINAL EXAM QUESTIONS 1. (10 points) Solve by using Cramer’s rule , for the following system 3ݔ ൅ 2ݕ ൅ ݖ ൌ 3 2ݔ ൅ 4ݕ ൅ 3ݖ ൌ 4 െݔ ൅ ݕ ൅ 5ݖ ൌ 8 2. (15 points) An economy is based on three sectors, agriculture (A), manufacturing (M), and energy (E). Production of a dollar’s worth of agriculture requires an input of \$0.20 from the agriculture, \$0.20 from manufacturing and \$0.20 from the energy. Production of a dollar’s worth of manufacturing requires an input of \$0.40 from the agriculture, \$0.30 from the manufacturing, and \$0.10 from energy. Production of a dollar’s worth of energy requires an input of \$0.30 from the agriculture, \$0.10 from the manufacturing, and \$0.10 from the energy sector.
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