Section 2.2 – Solving Systems of Linear Equation I
1
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 GaussJordan 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
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Section 2.2 – Solving Systems of Linear Equation I
2
Example:
The augmented matrix is:


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

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