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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 GaussJordan Elimination, we'll
get a row of all zeros except for the last
number.
Example:
If the augmented matrix reduces
to
1020
0001
0000
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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View Full Document Example:
12
24
23
xx
+=
4
3
21
R
R
−
4
00
1
−
For the last equation, we get 0 = 1.
Obviously this can't happen, so this system
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This note was uploaded on 07/16/2008 for the course MATH 1114 taught by Professor Jhengland during the Fall '08 term at Virginia Tech.
 Fall '08
 JHENGLAND
 Linear Algebra, Algebra, GaussJordan Elimination

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