set_2_problem - Problem Set 2 MMAE 501 Engineering Analysis...

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Problem Set # 2 MMAE: 501 Engineering Analysis I Kevin W. Cassel Mechanical, Materials and Aerospace Engineering Department Illinois Institute of Technology 10 West 32nd Street Chicago, IL 60616 [email protected] Problem Reference Problem # 1: Hilderbrand, Chapter 1, Problem 11 Problem # 2: Hilderbrand, Chapter 1, Problem 35 Problem # 3: Hilderbrand, Chapter 1, Problem 39 Problem # 4: Jeffrey, Section 2.2, Problem 26 Problem # 5: Jeffrey, Section 2.5, Problem 27 Problem # 6: Jeffrey, Section 2.5, Problem 28 Problem # 7: Jeffrey, Section 2.7, Problem 5 Problem # 8: Jeffrey, Section 3.9, Problem 9 c 2007 Kevin W. Cassel 1
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Problem # 1 Determine those values λ for which the following set of equations may possess a nontrivial solution: 3 x 1 + x 2 - λx 3 = 0 4 x 1 - 2 x 2 - 3 x 3 = 0 2 λx 1 + 4 x 2 + λx 3 = 0 . For each permissible value of λ , determine the most general solution. Problem # 2 a) By investigating ranks of relevant matrices, show that the following set of equations possesses a one-parameter family of solutions: 2 x 1 - x 2 - x 3 = 2 x 1 + 2 x 2 + x 3 = 2 4 x 1 - 7 x 2 - 5 x 3 = 2 . b) Determine the general solution. Problem # 3 Determine whether the vector { 6 , 1 , - 6 , 2 } is in the vector space generated by the vectors
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