# rec09 - Recitation Problems – Week 8 440:127 – Fall...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 Jacobi’s iterative method and can beIn this form, the system can be solved iteratively....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online