rec09 - Recitation Problems Week 8 440:127 Fall 2011 S. J....

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Unformatted text preview: Recitation Problems Week 8 440:127 Fall 2011 S. J. Orfanidis Please do the following problems during your recitation session, including any additional problems given to you by your TA. 1. Consider the linear system: 4 x 1 + 2 x 2 + x 3 = 11 x 1 + 2 x 2 = 3 2 x 1 + x 2 + 4 x 3 = 16 Cast it in the matrix form A x = b and solve it. Next, express each of the x 1 ,x 2 ,x 3 in terms of the other two and rewrite these equations in the form: x 1 = 2 . 75 . 5 x 2 . 25 x 3 x 2 = 1 . 5 + . 5 x 1 x 3 = 4 . 5 x 1 . 25 x 2 x 1 x 2 x 3 = . 00 . 50 . 25 . 50 . 00 . 00 . 50 . 25 . 00 x 1 x 2 x 3 + 2 . 75 1 . 50 4 . 00 or, x = B x + c , B = . 00 . 50 . 25 . 50 . 00 . 00 . 50 . 25 . 00 , c = 2 . 75 1 . 50 4 . 00 , x = x 1 x 2 x 3 In this form, the system can be solved iteratively. This is known as Jacobis iterative method and can beIn this form, the system can be solved iteratively....
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