A 2 7 b 1 2 0 c t 5 3t 15 t for all real

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online