Lecture19 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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Unformatted text preview: Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00 2 Lecture 19 Lecture 19 Last time: Midterm: solutions and discussions Today: Today The inverse of a matrix Iterative methods for solving sytems of linear equations Gauss-Siedel Jacobi Next Time Relaxation Non-linear systems The inverse of a square If [ A ] is a square matrix, there is another matrix [ A ]-1 , called the inverse of [ A ], for which [ A ][ A ]-1 =[ A ]-1 [ A ]=[I] The inverse can be computed in a column by column fashion by generating solutions with unit vectors as the right-hand-side constants: A [ ] x 1 { } = 1 A [ ] x 2 { } = 1 A [ ] x 3 { } = 1 A [ ]- 1 = x 1 x 2 x 3 [ ] Canonical base of an n-dimensional vector space 100000 010000 001000 ....
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This note was uploaded on 02/17/2012 for the course EGN 3420 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Lecture19 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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