linear 1.1-1.2

consistent system

when a linear system has at least 1 solution

row equivalent matricies

occurs if a sequence of row operations transforms one matrix into the other

echelon form conditions

all zero rows are at bottom of matrix, leading entry is to the right of leading entry in row above it, all entries below a leading entry are zero

row reduction algorithm

use elementary row operations to transform matrix into echelon form or RREF

row reduced echelon form (RREF)

every leading entry is 1, each leading 1 is the only nonzero entry in its column

leading entry

the first nonzero entry in each row

pivot position

location in matrix that corresponds to a leading 1 in the RREF of that matrix

pivot column

column that contains a pivot position

basic variable

variable corresponding with pivot columns

free variable

variable corresponding to non-pivot columns

unique solution

when system is consistent and has no free variables

infinitely many solutions

when the system is consistent and has at least 1 free variable

no solution

when the system is inconsistent