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# week04 - Math 43 Fall 2007 B Dodson Week 4 See homework...

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Math 43, Fall 2007 B. Dodson Week 4: See homework schedule, attached. We solve systems of linear equations by replacing the system with the augmented matrix of the system, and applying elementary row operations. There are three elementary row operations: 1. switch two rows ( R i R j ) 2. multiply a row by a non-zero number ( kR i , k = 0) 3. replace a row by itself plus a multiple of another row ( R j + kR i ). Our prefered method is Gauss-Jordan elimination which combines Gauss elimination with row operations that do the “back substitution” steps. See the text for Example 2.9 (pg. 70-71) and Example 2.13 (pg. 74-75, Ex. 2.11 and pg. 77-78). We have two different notions of what simplifying the augmented matrix by using row operations means. We may start by getting a row echelon matrix (for Gaussian elimination), but we prefer to continue simplifying until we have a reduced row echelon matrix (for Gauss-Jordan). Here’s our quiz from Wednesday’s class.

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2 MATH 43 Solutions to 4th Quiz September 19, 2007 NAME: (Last, First) 2. Find the system of equations with the aumented matrix
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