e1s-415 - Name ID Number MTH 415 Exam 1 Read each question...

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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 Σ Solution Problem 1: We use Gauss-Jordan’s 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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This note was uploaded on 10/28/2010 for the course MATH Math 415 taught by Professor Dr.gabrielnagy during the Spring '09 term at Michigan State University.

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e1s-415 - Name ID Number MTH 415 Exam 1 Read each question...

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