1.2 Row Reduction and Echelon Form

Question 1

leading entry

Answer 1

leftmost nonzero entry in a nonzero row

Question 2

echelon form / row echelon form

Answer 2

1. all nonzero rows are above any rows of all zeros
2. each leading entry of a row is in a column to the right of the leading entry of the row above it
3. all entries in a column below a leading entry are zeros

Question 3

reduced (row) echelon form

Answer 3

all the properties of echelon form as well as

1. the leading entries in each nonzero row is 1
2. each leading 1 is the only nonzero entry in its column

IS UNIQUE

Question 4

echelon matrix

Answer 4

a matrix in its echelon form

Question 5

reduced echelon matrix

Answer 5

a matrix in its reduced echelon form

Question 6

row reduced

Answer 6

transformed by elementary row operations

Question 7

pivot position

Answer 7

corresponds to a leading 1 in the reduced echelon form of the matrix

Question 8

pivot column

Answer 8

a column of a matrix that contains a pivot position

Question 9

pivot

Answer 9

a nonzero number in a pivot position that is used as needed to create zeros via row operations

Question 10

forward phase

Answer 10

combination of steps that transforms a matrix into its echelon form

Question 11

backward phase

Answer 11

combination of steps that transforms an echelon matrix to reduced echelon matrix

Question 12

basic variables

Answer 12

the variables that correspond to the pivot columns in the matrix

Question 13

free variables

Answer 13

variable that does not correspond to a pivot column

Question 14

unique solution

Answer 14

no free variable, only one solution