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 ² The inverse of a matrix ² Iterative methods for solving sytems of linear equations ± Gauss-Siedel ± Jacobi ± Next Time ² Relaxation ² Non-linear systems
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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
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The response of a linear system ± The response of a linear system to some stimuli can be found using the matrix inverse.
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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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