Question

1 1 1 1 Determine whether each of the following augmented matrices are in reduced row echelon form (RREF). 1 2 0 3 0 1 0 0 0 5 0 0 0 1 5 (a) (b) 0 36 0 0 0 0 | -3 0 0 1 / 4 0 0 0 0 0 0 0 0 | 3 0 0 0 0 2 53 18 (c) (d) 0 -1 0 4 / 9 0 0 0 0 10 0 0 0 3 7 0 0 -2 2 1 1 1 1 1 1

Answer 1

(a) it is in RREF,

because, the leading elements in each non-zero row is 1, and that column which contains the leading 1 of some row, has no other non-zero elements. And, the zero row is placed at the bottom (after all the non-zero rows)

(b) it is not in RREF,

because, if we consider the leading 1 of the third row, the third column (as it contains the leading 1 of the third row) must not contain any other non-zero element, but it has a '3' right above the '1'

(c) it is not in RREF,

because, the zero row is the third row, followed by a non-zero row, which is not desired.

(d) it is in RREF,

because, the leading elements in each non-zero row is 1, and that column which contains the leading 1 of some row, has no other non-zero elements. And, the zero row is placed at the bottom (after all the non-zero rows)