Lecture Notes 3

Lecture Notes 3 - Lecture 03 Lecture 03: Systems of Linear...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 03 1 September 11, 2007 Outline: Gaussian Elimination ( Ax =b Ux =c ) 1) Review mechanics 2) Review modes of failures 3) The general pattern of GE 3) GE using Matrices (E and P) 4) General Rules of Matrix-Matrix Operations Addition: (A+B) Matrix Multiplication: AB Matrix Powers: A p Lecture 03: Systems of Linear Equations #2: Gaussian Elimination Gaussian Elimination on a 3x3 system of equations: Example ( with row exchange): x + 2y + 4z = 1 2x + 4y + 2z = 2 6x + 10y - z = 8 Matrix Vector form: Augmented Matrix form: Gaussian Elimination on a 3x3 system of equations: [ [ 1 2 4 1 2 4 2 2 6 10 -1 8 A b Step 1: Step 2: Step 3: Step 4: Example 2: Example 1: Failure of Gaussian Elimination (review): The overall Pattern of Gaussian Elimination: A recursive Algorithm that reduces Ax =b to Ux =c If successful: U will contain n pivots on the diagonal (unique solution) If Fails: U will contain at least 1 zero on the diagonal (no or solutions) Gaussian Elimination using matrices:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

Lecture Notes 3 - Lecture 03 Lecture 03: Systems of Linear...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online