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CSC_349_HANDOUT#17 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 17 MATRIX INVERSES This topic is discussed in the textbook in Section 10.2 in terms of an LU decomposition (which is just another way of interpreting Gaussian elimination). We are omitting all of Chapter 10. The following material is similar to that in Section 10.2 but is not described in terms of an LU decomposition. If it is necessary to compute A 1 , this is most efficiently and accurately done using Gaussian elimination (with partial pivoting) and the fact that I A A = 1 . Suppose that a matrix A is given. If the (unknown) column vectors of A 1 are denoted ) ( ) 2 ( ) 1 ( , , , n x x x K then [ ] = × = 1 0 0 0 1 0 0 0 1 | | | ) ( ) 2 ( ) 1 ( 1 L M O M L L L n x x x A A A , and the vectors x ( i ) can be determined by solving the n linear systems = = = 1 0 0 , , 0 1 0 , 0 0 1 ) ( ) 2 ( ) 1 ( M L M M n x A x A x A .
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