matlabassignmnet1 - x 6 = 3 Check that Ax = b 3 The purpose...

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Math 3353 Matlab Assignment 1 - Due 9/25/09 T. Hagstrom 1. Create a 6 × 4 matrix A , a 4 × 3 matrix B , and two different 3 × 3 matrices C and D . Using them illustrate the following laws of matrix algebra: Associative ( AB ) C = A ( BC ) Distributive B ( C + D ) = BC + BD Commutativity of Addition C + D = D + C Noncommutativity of Multiplication CD 6 = DC Additive Identity A + 0 = A Multiplicative Identity IB = BI = B Scalar Multiplication B ( rD ) = rBD (Choose r 6 = 0 , 1.) Transposition of Sums ( C + D ) T = C T + D T Transposition of Products ( AB ) T = B T A T Double Transposition ( B T ) T = B 2. Use the randn command to create a random 4 × 6 matrix, A . Use the null command to compute two independent null vectors. As they were chosen at random, it is quite likely that the first four columns of A are independent. Use this fact to compute a particular solution of Ax = b where b is a randomly chosen 4-vector. (This particular solution will have x 5 = x 6 = 0.) Now add on appropriately chosen null vectors to generate a solution with x 5 = - 2 and
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Unformatted text preview: x 6 = 3. Check that Ax = b . 3. The purpose of this problem is to set up and solve a larger version of the heat transfer problem considered in problems 33 and 34 in Section 1.1. Suppose there are 16 instead of 4 interior nodes, arranged in a 4 × 4 lattice. Assume in addition 4 nodes on each edge, with temperatures of 10 on the left boundary, 20 at the top, 40 on the right, and 30 on the bottom. The equations are that each temperature is the average of its four neighbors. Set up the equations and solve them using Matlab. You can number the nodes anyway you like, but you should obtain a system of 16 equations in 16 unknowns. Draw the lattice and write down the temperature at each node to at least 4 digits of accuracy. What are the maximum and minimum temperatures and where do they occur? 1...
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This note was uploaded on 04/05/2010 for the course MATH 3353 taught by Professor Hagstrom during the Fall '09 term at Southern Methodist.

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