EXAMPLE 1: m>n, unique solution with a redundant row arising mid-elimination
Solve the below system of equations using Gauss elimination.
Forming the augmented matrix and applying Gauss elimination:
⇒
[
]
⇒
[
⏟
⇒
]
[
⏟
]
⇒
⏟
[
]
[
⏟
]
There are no inconsistencies in the row-echelon form. Therefore, the system has at least one solution. In the rowechelon form, one row is redundant leaving 4 linearly independent equations. Since there is the same number of linearly
independent equations as the number unknowns (4), this system has a unique solution.
Applying back-substitution:
or
[ ]
ME 210/Spring 2014/Section 01/Merve Erdal
[
]
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EXAMPLE 2: m>n, inconsistency
Solve the below system of equations using Gauss elimination.
Forming the augmented matrix and applying Gauss elimination:
⇒
[
]
⏟
⇒
[
]
⏟
[
]
STOP
The 3rd row indicates an inconsistency, i.e.
which is not possible.
Therefore, there is no need to continue the elimination; this system has no solution.
ME 210/Spring 2014/Section 01/Merve Erdal
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