MA 35100 Lecture Notes - Lecture 8: If And Only If, Linear Combination
Document Summary
**i . se#iph94: recall : we said 0 rows appearing during ge means that the original equations are 1in . dependent. " the rank of a system of linear equations is the number of nonzero. Def rows in any eschelon form of the augmented matrix : can be thought of as the number of equations remaining after 1in . dependent ones have been removed . Theorem 1. 7 ( more unknowns theorem) : a system of les with more unknowns than equations has either no solutions or infinitely many solutions . " if you can see one solution [ read it off) in a system where there are more unknowns than equations , there must be infinitely. If it"s inconsistent , the reduced form has a row [0 - . If it"s consistent , all leading is are in columns corresponding to variables . So , # pivot variables = # leading is # rows < # variables.
