MATH1503 Chapter Notes - Chapter 1-8: Row Echelon Form, Invertible Matrix, Elementary Matrix
Document Summary
Each matrix is row equivalent to one and only one reduced echelon matrix. Pivot position a _____________ in a matrix a is a location in a that corresponds to a leading 1 in the reduced echelon form of a. A pivot column is a column of a that contains a pivot position. Existence and uniqueness theorem a linear system is consistent iff the rightmost column of the augmented matrix is not a pivot column. That is, iff an echelon form of the augmented matrix has no row of the form [0 0 b] with b nonzero. If linear system is consistent, then the solution set contains either a unique solution, when there are no free variable or infinitely many solutions , when there is at least one free variable. The equation ax = b has a solution iff b is a linear combination of the columns of a.
