HOW TO REDUCE A MATRIX
Legal Row Operations: 1) Interchange 2 rows of the matrix 2)
Multiple every entry in a row by a constant. 3) Multiply every
entry in a row by a constant, then add that row to another row.
Note: Use operations 1)and 2) To create ones in a matrix. Use
operation 3) to create zeros.
Example 1. Reduce
654
321 Your goal is to transform it to
b
a
10
01
Since there is already a 1 in the upper left corner, the next
step is to create a zero where the 4 is. Multiply every entry in
row 1 by -4 and add those products to row 2.
Now the matrix should look like this:
630321
The next step is to create a 1 where the -3 is.
Step 2: Multiple each entry in row 2 by -1/3.
Now the matrix looks like this:
210
321 Finally, create a zero right above the 1 in row 2.
Step 3: Multiple every entry in row 2 by -2 and add those
products to row 1 :
210
101
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Example 2: Reduce
17552
4031
9321
Your goal is to transform it to
c
b
a
100
010
001
221 RRR + 3312 RRR + 1122 RRR + 332 RRR +
17552
4031
9321
17552
13310
9321
1110
13310
9321
111013310
35901
3321 RR 2233 RRR + 1139 RRR +
12200
13310
35901
6100
13310
35901
6100
5010
35901
6100
5010
19001
