Section 1.4 Inconsistent SystemsWith 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 102000010000the second row says 0x1+ 0x2+ 0x3= 1. That’s impossible! 0 can’t be 1. This system has no solution i.e. it’s inconsistent.
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