REF and RREF

Question 1

A matrix is in REF if:

Answer 1

• if the row is not entirely made of zeros, the first non-zero entry is a 1 (leading one)
• any all-zero rows are at the bottom
• leading ones are on the right of the leading one above

Question 2

A matrix is in RREF if

Answer 2

If the COLUMN with the leading one has zeros in every other entry
Can have a zero row

Question 3

Gauss algorithm (matrix -> REF)

Answer 3

• locate left most non-zero column
• swap rows to bring non-zero entry to top (pivot element)
• divide first row by pivot element to make a leading one
• add suitable multiples to rows so all entries below the leading one are zero
• repeat until in REF

Question 4

Gauss-Jordan algorithm (matrix -> RREF)

Answer 4

• use Gauss algorithm to make matrix into RREF
• work upwards from lowest non-zero row, clear entries above each leading one