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Unformatted text preview: t. Those which have solutions are called consistent, those with no 454 Systems of Equations and Matrices solution are called inconsistent. We also distinguish the two diﬀerent types of behavior among
consistent systems. Those which admit free variables are called dependent; those with no free
variables are called independent.4 Using this new vocabulary, we classify numbers 1, 2 and 3 in
Example 8.1.1 as consistent independent systems, number 4 is consistent dependent, and numbers
5 and 6 are inconsistent.5 The system in 6 above is called overdetermined, since we have more
equations than variables.6 Not surprisingly, a system with more variables than equations is called
underdetermined. While the system in number 6 above is overdetermined and inconsistent,
there exist overdetermined consistent systems (both dependent and independent) and we leave it
to the reader to think about what is happening algebraically and geometrically in these cases.
Likewise, there are both consistent and inconsistent underdetermine...
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