02-gaussjordan

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

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

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