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# ef2-415 - Name MTH 415 Practice Final Exam PID Number No...

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Name: PID Number: MTH 415 Practice Final Exam August 17, 2009 No calculators or any other devices are allowed on this exam. Read each question carefully. If any question is not clear, ask for clariﬁcation. Write your solutions clearly and legibly; no credit will be given for illegible solutions. Answer each question completely, and show all your work. If you present diﬀerent answers, then the worst answer will be graded. Signature: Problem Points Score 1 20 2 20 3 20 4 20 5 20 6 20 7 20 8 20 9 20 10 20 Σ 200 1

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1. (20 points) Consider the matrix A = 5 3 1 1 2 - 1 2 1 1 . Find the coeﬃcients ( A - 1 ) 21 and ( A - 1 ) 32 of the matrix A - 1 , that is, of the inverse matrix of A . Show your work.
(20 points) (a) Find k R such that the volume of the parallelepiped formed by the vectors below is equal to 4, where v 1 = 1 2 3 , v 2 = 3 2 1 , v 3 = k 1 1 (b) Set k = 1 and deﬁne the matrix A = [ v 1 , v

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ef2-415 - Name MTH 415 Practice Final Exam PID Number No...

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