1.4 - Section 1.4 Inconsistent Systems With 2X2 systems this occurs when we have parallel lines With 3X3 systems this occurs when we have parallel

1.4 - Section 1.4 Inconsistent Systems With 2X2 systems...

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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 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.