1. REDUCING MATRICES

2. A matrix that reduces to this
Can readily be interpreted

3. 1. Place 1 in the upper left
If you follow this order, you will not
waste time or go around in circles.
2. Place 0’s in the column under the red 1
3. Place second 1 on the diagonal
4. Place 0’s in the column under the blue 1
5. Place third 1 on the diagonal
6. Place 0 in the column under the green 1
7. Place fourth 1 on the diagonal
8. A 0 in the
upper right
triangle can be
placed at any
point after the 1
and the lower 0’s
have been placed
in its column

4. Consider this system.
First extract the coefficient matrix

5. +2 1 -1 0 -1 L1 becomes: First we want a 1 in this position.
Replace L1 with L L2
L1 becomes:

6. +2 L2 becomes 0 -1 -1 -4 Second we want 0’s in these positions.
Replace L2 with L L1 +2
L2 becomes
Second we want 0’s in these positions.

7. +1 L2 becomes 0 -1 -1 -4 L3 becomes 0 0 1 1
Replace L3 with L L1 +1
L2 becomes
Second we want 0’s in these positions.
L3 becomes
Replace L2 with L L1

8. Replace L2 with -1L2
L2 becomes
Third we want a 1 in this position.

9. Fourth we have a 0 in this position.
And a 1 in this position

10. -1 L2 becomes 0 1 0 3 Finally we need 0’s in these positions
Replace L2 with L L3 -1

11. L1 becomes
Replace L1 with L L2 +1
L2 becomes