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Section 2.2  Solving Systems of Linear Equations I
As you may recall from College Algebra, you can solve a system of linear equations in two variables
easily by applying the substitution or addition method.
Since these methods become tedious when
solving a large system of equations, a suitable technique for solving such systems of linear equations
of any size is the
GaussJordan elimination method
.
This method involves a sequence of
operations on a system of linear equations to obtain at each stage an equivalent system.
The Gauss
Jordan elimination method is complete when the original system has been transformed so that it is in
a certain standard form from which the solution can be easily read.
Augmented Matrices
Matrices
are rectangular arrays of numbers.
We will use these to solve systems of equation in 2 or
more variables.
Example:
Given
2
2
27
5
8
3
22
6
4
2
=
+
+

=
+
+
=
+
+
z
y
x
z
y
x
z
y
x
.
The coefficient matrix is:

2
1
1
5
8
3
6
4
2
.
The augmented matrix is:

2
27
22



2
1
1
5
8
3
6
4
2
Example:
The augmented matrix is:


8
0
2
6
1
1
0
5
5
4
1
2
. Write down the system.
Example:
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 Spring '08
 CONSTANTE
 Math, Linear Equations, Addition, Equations, Systems Of Linear Equations, Elementary algebra

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