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 nonzero 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
GaussJordan elimination
which combines
Gauss elimination
with row
operations that do the “back substitution” steps.
See the text for Example 2.9 (pg. 7071) and
Example 2.13 (pg. 7475, Ex. 2.11 and pg. 7778).
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 GaussJordan).
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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 Spring '08
 Dodson
 Linear Equations, Equations, Gaussian Elimination, Systems Of Linear Equations, Elementary algebra, Row Echelon matrix

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