test3 - Differential Equations/ Linear Algebra Mid term...

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Unformatted text preview: Differential Equations/ Linear Algebra Mid term Test -III MTH 2201 Duartion: 1 hour 4/21/2005 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. Consider the system of equations : 5x - 4y = 0 x + 2z = 0 2y + 5z = 0. Use Gauss Jordon Elimination Method to find the free variable and find all the solutions of the system. (No credit will be given for solutions found without using Gauss -Jordon elimination. Clearly indicate the row operations used.) [6] 2. Find the eigen values and eigen vectors of the coefficient matrix of the system in Q.1. [5] 3. Solve the system k1 - 9k2 + 2k3 = 2 k1 - 5k2 + 2k3 = 0. 4. Find the general solution of the system of first order differential equations [6] x y z = 5x - 4y = x + 2z = 2y + 5z. [3] 1 1 5. Construct a 3 3 matrix whose column space contains 1 , 0 , but 0 1 1 [6] not 1 . 1 6. Let M2 be the vector space of all 2 2 matrices with the usual matrix addition and scalar multiplication. Let W = {A M2 |A-1 exists }. Show that [4] W is NOT a subspace of M2 . 1 ...
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