inverse - Lecture Note 3-1 Dr. Jeff Chak-Fu WONG Department...

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Unformatted text preview: Lecture Note 3-1 Dr. Jeff Chak-Fu WONG Department of Mathematics Chinese University of Hong Kong [email protected] MAT 2310 Linear Algebra and Its Applications Fall, 2007 Produced by Jeff Chak-Fu WONG 1 S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS SOLUTIONS OF LINEAR SYSTEMS OF EQUATIONS 2 A M ETHOD FOR F INDING THE INVERSE A METHOD FOR FINDING THE INVERSE 3 Let A be an n × n matrix. If A is invertible, then there is a matrix B with AB =         1 1 . . . 1         Let the columns of B be the vectors x 1 , x 2 , ··· , x n . So B = h x 1 x 2 ··· x n i and AB = h A x 1 A x 2 ··· A x n i . A METHOD FOR FINDING THE INVERSE 4 We want AB = I n , so we wish to find the vectors x 1 , x 2 , ··· , x n such that A x 1 =            1 . . .            , A x 2 =            1 ....
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This note was uploaded on 05/18/2010 for the course MATHEMATIC MAT2310 taught by Professor Dr.jeffchak-fuwong during the Spring '06 term at CUHK.

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inverse - Lecture Note 3-1 Dr. Jeff Chak-Fu WONG Department...

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