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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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