02-gaussjordan

# 02-gaussjordan - 9/29/2004, MATRICES AND GAUSS-JORDAN Math...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 9/29/2004, MATRICES AND GAUSS-JORDAN Math 21b, O. Knill HOMEWORK: 1.2: 6,12,18,20,30,32*,38* Due: Fri 10/1/2004 MATRIX FORMULATION. Consider the sys- tem of linear equations 3 x- y- z = 0- x + 2 y- z = 0- x- y + 3 z = 9 The system can be written as A~x = ~ b , where A is a matrix (called coefficient matrix ) and and ~x and ~ b are vectors . A = 3- 1- 1- 1 2- 1- 1- 1 3 , ~x = x y z , ~ b = 9 . (( A~x ) i is the dot product of the i th row with ~x ). We also look at the augmented matrix where one puts separators for clarity reasons. B = 3- 1- 1 |- 1 2- 1 |- 1- 1 3 | 9 . MATRIX JARGON. A rectangular array of numbers is called a matrix . If the matrix has m rows and n columns , it is called a m n matrix. A matrix with one column only is called a column vector , a matrix with one row a row vector . The entries of a matrix are denoted by a ij , where i is the row and j is the column. In the case of the linear equation above, the matrix A is a square matrix and the augmented matrix B above is a 3 4 matrix. m n GAUSS-JORDAN ELIMINATION. Gauss-Jordan Elimination is a process, where successive subtraction of multiples of other rows or scaling brings the matrix into reduced row echelon form...
View Full Document

## This note was uploaded on 04/06/2008 for the course MATH 21B taught by Professor Judson during the Spring '03 term at Harvard.

Ask a homework question - tutors are online