DEtest12006

DEtest12006 - Differential Equations/ Linear Algebra Mid...

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Unformatted text preview: Differential Equations/ Linear Algebra Mid term Test -I MTH 2201 Duartion: 1 hour 6/1/2006 Max. Credit: 30 points Answer all the questions. No credit will be given if only the answer is written without showing the relevant supporting work. Write legibly. The numbers at the end of each question indicate the maximum credit for the corresponding question. 1 2 0 1. Find the eigen values and eigenvectors of the matrix 0 1 -2 . 2 2 -1 2. Let A = AT . 3. Use Cramer's rule to find y without solving for x and z x + 2y + 3z = -2 3x - y + z = 1 -x + 4y - 2z = -3 [6] 4. The Augmented matrix for a system of linear equations is given by [8] 2 0 2 3 . Find the eigen values of A and the eigenvectors of A and [4] 1 1 -3 2 1 4 0 3 . 0 1 0 0 0 1 2 Find all solutions of the system. 5. A = 1 0 -5 2 (a) Find elementary matrices E1 and E2 such that E2 E1 A = I (b) Write A-1 as a product of two elementary matrices. (c) Write A as a product of two elementary matrices. [4] [3+2+3] 1 ...
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