section17 - Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1...

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Unformatted text preview: Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1 Lecture Notes Fall 2007 Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Chapter 1 1.7: LU-Factorization Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 1.7: LU-Factorization Example 4 From Section 1.2, Again Consider the system of equations in three variables x 1 , x 2 and x 3 : 2 x 1 + x 2- x 3 = 1 x 1 + x 2 + x 3 = 6- 3 x 1 + 2 x 2 + 4 x 3 = 13 This can be written as a single matrix equation AX = B , with A = 2 1- 1 1 1 1- 3 2 4 , X = x 1 x 2 x 3 , B = 1 6 13 . Now consider the matrices L = 1 0 0 1 / 2 1 0- 3 / 2 7 1 and U = 2 1- 1 0 1 / 2 3 / 2- 8 . Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 1.7: LU-Factorization A = LU L is a lower triangular matrix and U is an upper triangular matrix. You can check that A = LU . This is called an LU factorization of A . It can be used to solve the system AX = B in a different, more...
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This note was uploaded on 06/22/2008 for the course ENGINEERIN MAT188 taught by Professor Burbula during the Fall '07 term at University of Toronto- Toronto.

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section17 - Chapter 1 MAT188H1F Lec03 Burbulla Chapter 1...

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