Chapter 1 Definitions

Definitions

Pivot

the leftmost nonzero entry in that row

Row Echelon Form

1. all rows consisting only of zeros are at the bottom,

2. and the pivot of each nonzero row in the matrix is in a column to the right of the pivot of the row above it.

Reduced Row Echelon Form

1. the matrix is in echelon form

2. the pivot in each nonzero row is 1, and

3. each pivot is the only nonzero entry in its column

Basic Variable

x_i is the (Term) for the system if the i^th column of rref(C) has a pivot

Free Variable

x_i is the (Term) for the system if the i^th column of rref(C) does not have a pivot.

Consistent

what a system of linear equations is called if it has at least one solution

Inconsistent

what a system of linear equations is called if it has no solutions

Parametric description of the solution set to the rref of the system {{1, 0, 0, 1, 0}, {0, 1, 1, 4, -1}, {0, 0, 0, 0}}

{(-3w, w, -1-4w-z, z, w) : z,w∈ℝ)}