Section 1.4
Inconsistent Systems
With 2X2 systems, this occurs when we
have parallel lines.
With 3X3 systems, this occurs when we
have parallel planes.
These should be obvious.
Specifically,
when doing Gauss-Jordan Elimination, we'll
get a row of all zeros except for the last
number.
Example:
If the augmented matrix reduces
to
1
0
2
0
0
0
0
1
0
0
0
0
the second row says 0x
1
+ 0x
2
+ 0x
3
= 1.
That’s impossible!
0 can’t be 1.
This
system has no solution i.e. it’s inconsistent.

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