e1s-415 - Name: ID Number: MTH 415 Exam 1 February 04, 2009...

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Unformatted text preview: Name: ID Number: MTH 415 Exam 1 February 04, 2009 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. If you present different answers for the same problem, the worst answer will be graded. Answer each question completely, and show all your work. 1. (20 points) Find the general solution to the homogeneous linear system with coefficient matrix A = 1 3- 1 5 2 1 3 3 2 4 1 , and write this general solution in vector form. # Score 1 2 3 4 5 Solution Problem 1: We use Gauss-Jordans method to find the general solution to the system A x = . 1 3- 1 5 2 1 3 3 2 4 1 1 3- 1 5- 5 5- 10- 7 7- 14 1 3- 1 5 1- 1 2 1- 1 2 1 2- 1 1- 1 2 , therefore, the solution is x 1 =- 2 x 3 + x 4 x 2 = x 3- 2 x 4 x 3 :free x 4 :free. x = - 2 1 1 x 3 + 1- 2 1 x 4 . 2. (a) (10 points) Find a value of the constants h and k such that the non-homogeneous linear system below is consistent and has one free variable....
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e1s-415 - Name: ID Number: MTH 415 Exam 1 February 04, 2009...

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