**University of Florida, COT 3502**

**Excerpt:** ... clearly show your work! COT 3502 Computer Model Formulation Spring 2008 2 2. (20 points) Perform the LU-decomposition of the following matrix: A= 12 3 5 Your answer should contain the matrices L (or L1 ) and U (or U 1 ) of the LU-decomposition. 3. (20 points) Obtain inverse of the following matrix: 0 1 A= 0 0 0 0 0 1 1 0 0 0 0 0 . 1 0 Bonus 5 points if you obtain the ** inverse matrix ** without using Gaussian elimination, GaussJordan method, or the LU-decomposition. You should explain how you obtained the ** inverse matrix **. 4. (20 points) Are vectors 1 a = 2 , 1 3 b = 4 , 1 3 and c = 4 2 linearly independent? Justify your answer! 5. (20 points) Consider the following system of nonlinear equations x1 + x2 x3 = 1, 2x2 + 2x1 x3 = 2, 4x3 x1 x2 = 3. You are given the following guess for the solution of this system of equations: x1 = x2 = (0) x3 = 0. Perform one step of the Newton-Raphso ...