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assignment3 - Math 151 Summer 2009 Assignment 3 begins Due...

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Unformatted text preview: Math 151 Summer 2009 Assignment 3 begins. Due Date: Tuesday, July 7 2009, in class, before the lecture Reminder: There will be no class on Friday July 3, 2009. 1. De ne the matrices A, B , and C as: A= 131 211 −1 1 B = 0 −1 C = 10 23 35 (a) [2 marks] Solve the following matrix equation for the matrix D. 1 AB − CD = 0 2 (b) [1 mark] What is the size of matrix D? (c) [3 marks] Find the inverse of C using the method shown in class. (d) [2 marks] Use parts (a) and (b) to nd matrix D. 1 2. De ne the matrices X and T as: X= x1 x2 x3 0.6 0.3 0.1 T = 0.4 0.3 0.3 0.3 0.3 0.4 You will nd the values of x1, x2, x3 satisfying X = XT and x1 + x2 + x3 = 1 through the following steps: (a) [3 marks] From the matrix equation X = XT , nd three linear equations involving x1, x2, x3. (b) [4 marks] Consider the system of four equations, made up of the three equations from (a) together with the equation x1 + x2 + x3 = 1. Solve this system of four equations for x1, x2, x3 using Gauss-Jordan elimination. 3. [5 marks] Solve the following system using Gauss-Jordan elimination. 3x1 + 2x2 + 12x3 + 2x4 + 15x5 + 14x6 = 13 2x1 + x2 + 7x3 + x4 + 9x5 + 8x6 = 7 2x1 + 2x2 + 10x3 + 3x4 + 14x5 + 15x6 = 15 2 ...
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