Matrices
1
Gaussian Elimination is also called
GaussJordan Reduction
. Either term refers to using the standard
row operations to find the
rref
form of the matrix.
© Arizona State University, Department of Mathematics and Statistics
1 of
3
Objectives:
At the end of this lesson, you should be able to:
1. Create a
matrix
from a linear system
2. Identify the various kinds of matrices we can create from them.
3. Define
Gaussian Elimination
within matrices
4. Apply
Gaussian Elimination
to a
matrix.
Background
Remember synthetic division? It made polynomial division
simpler by relying only on the position of the various degrees of
the variable.
It’s not an uncommon practice in math to let position dictate size,
degree or otherwise relate to a number such as a coefficient. We
do it with numbers all the time. That’s how we know that 10001
is a lot more than 101.
We do exactly the same thing with linear systems. Think back to
all of our Gaussian Conventions. We always said we would add
or otherwise combine the columns of like variables. If we just
drop out the variables, we create an array of coefficients or
constants.
As long as we don’t jumble the order on any row, position alone
should allow us to do the various row operations.
You may have already done this in the setup for linear
optimization. However, it won’t hurt to review the process.
Gaussian
1
Elimination
in Matrices
Take a look at this system:
1
1
2
3
2
1
2
3
3
1
2
3
:
3
3
5
: 2
4
2
1
:
4
5
2
2
r
x
x
x
r
x
x
x
r
x
x
x

+
=

+
=

+
=
Rectangular arrangements of numbers are called
matrices.
(
Matrix
is the singular). We can create a number of
arrays from this system. Suppose we decide to just look at the coefficients. The system
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 Spring '12
 DavidGlenn
 Algebra, Gaussian Elimination, Matrices, Row echelon form, Department of Mathematics and Statistics

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