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

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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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 0 0 A [ ] x 2 { } = 0 1 0 A [ ] x 3 { } = 0 0 1 A [ ] 1 = x 1 x 2 x 3 [ ]

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Canonical base of an n-dimensional vector space 100……000 010……000 001……000 ……………. 000…….100 000…….010 000…….001