Lecture 14

Question 1

what has to be true for a matrix to be in REF (row echelon form)

Answer 1

1. all non-zero rows are above any row of all zeros
2. each leading (non-zero)entry in a column is to the right of the leading (non-zero)entry of the row above it

Question 2

when is a matrix in RREF (reduced row echelon form)

Answer 2

1. it is in REF
2. all leading entries(pivots) are 1, called leading 1
3. in the column with a leading 1, all other values are 0

Question 3

a pivot is also known as

Answer 3

leading entries

Question 4

what is a leading variable(dependant)

Answer 4

if the i’th column has a pivot, than x_i is a leading variable

Question 5

what is a leading free variable (independent)

Answer 5

if the i’th column has no pivot, than x_i is a free variable

Question 6

when is a system inconsistent

Answer 6

if at least 1 row is structured [ zero’s | non-zero] its ok if zero is on the right side of the argument column though