Reduced Row Echelon Form

Question

Compute the reduced row echelon form of each of the follow matrices:

(a)

[ 2 1 ]

[ -3 -2 ]

(b)

[ 3 -3 -3 ]

[ 2 -3 -4 ]

(c)

[ 2 2 ]

[ 3 0 ]

[ 1 0 ]

(d)

[ 1 -2 0 ]

[ -2 4 -1 ]

[ 2 -4 -1 ]

Answer 1

a.

1 0

0 1

b.

1 0 1

0 1 2 operations r1-r2->r1, r2-2r1->r2, -1/3 r2->r2

c.

1 0

0 1

0 0 operations: r3 interchange r1, r3 interchange r2, r2-2r1->r2, r3-3r1,r3

d.

1 -2 0

0 0 1

0 0 0 operations: r2+2r1->r2, r3-2r1->r3, interchange r2 and r3, -1 *r2->r2