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

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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

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S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS 2
A M ETHOD FOR F INDING THE INVERSE A M ETHOD FOR F INDING THE INVERSE 3

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Let A be an n × n matrix. If A is invertible, then there is a matrix B with AB = 1 0 0 0 0 1 0 0 0 0 . . . 0 0 0 0 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 M ETHOD FOR F INDING 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 0 0 . . . 0 , A x 2 = 0 1 0 . . . 0 , · · · , A x n =

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