Section 2.3
Solving Systems of Linear Equations II
In the previous section we studied systems with unique solutions.
In this section we will
study systems of linear equations that have infinitely many solutions and those that have
no solution.
We also will study systems in which the number of variables is not equal to
the number of equations in the system.
A System of Equations with an Infinite Number of Solutions
Example 1:
The following augmented matrix in row-reduced form is equivalent to the
augmented matrix of a certain system of linear equations.
Use this result to solve the
system of equations.
a.
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
−
0
0
0
0
2
5
1
0
3
1
0
1
b.
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
−
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
1
c.
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎝
⎛
−
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
3
1
0
1
0
Section 2.3 – Solving Systems of Linear Equations II
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