section13 (2) - Chapter 1 MAT188H1F Lec03 Burbulla Chapter...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

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 Homogeneous Systems Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Homogeneous Systems What Is A Homogeneous System of Equations? If all the constants to the right of the equal signs in a system of linear equations are zero, then the system is called a homogeneous system of linear equations. That is, the augmented matrix of a homogeneous system looks like ( A | O ) where A = [ a ij ] is the m × n matrix of coefficients, and B = O is the all-zero m × 1 column vector of constants. Note: a homogeneous system of equations is consistent; there is always at least one solution, namely x 1 = 0 , x 2 = 0 , x 3 = 0 , . . . , x n = 0 . This is called the trivial solution. Chapter 1 Lecture Notes MAT188H1F Lec03 Burbulla Chapter 1 Homogeneous Systems Example 1 Consider the system of equations x 1- 2 x 2 + x 3 + x 4 = 0- x 1 + 2 x 2 + x 4 = 0 2 x 1- 4 x 2 + x 3 = 0 It’s augmented matrix is 1- 2 1 1- 1 2 0 1 2- 4 1 0 Row reduction gives...
View Full Document

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.

Page1 / 5

section13 (2) - Chapter 1 MAT188H1F Lec03 Burbulla Chapter...

This preview shows document pages 1 - 3. Sign up to view the full document.

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