# Matrix as a product of elementary matrices

1. Sep 7, 2009

### philnow

1. The problem statement, all variables and given/known data

Sorry for the double post, I couldn't re-edit the topic on my earlier post.

The assignment is to represent the following matrix as a product of elementary matrices:

1 3 5
3 10 11
-2 -7 -7

I reduced this matrix down to the identity matrix I using elementary row operations, which I recorded. I'll paste these here:

1)row 2 = row2 - 3row1
2)row 3 = row3 + 2row1
3)row 3 = row3 + row2
4)row 3 = -1*row3
5)row 1 = row1 - 3row2
6)row 1 = row1 - 17row3
7)row 2 = row2 - 4row3

The idea is now to represent each operation as an elementary matrix, and the product of the inverses of these matrices should give me my original matrix, correct?

1 0 0
3 1 0
0 0 1

1 0 0
0 1 0
0 -2 1

1 0 0
0 1 0
0 -1 1

1 0 0
0 1 0
0 0 -1

1 3 0
0 1 0
0 0 1

1 0 17
0 1 0
0 0 1

1 0 0
0 1 -4
0 0 1

the above matrices are the inverses of these row operations in elementary matrix form (I THINK!)(1-7 top to bottom). Here is the problem... when I multiply these matrices out (using matlab) I'm getting the same answer every time:

1 3 5
3 10 11
0 -3 13

the last row is clearly off, while the rest is right on... This is driving me crazy! Any help?

2. Sep 8, 2009

### njama

First, I reduced the matrix to identity matrix and spotted one error:
7) should be row2+4row3

Also, you got wrong the inverse matrix of the 2) elementary matrix

It should be:

1 0 0
0 1 0
-2 0 1

3. Sep 8, 2009

### philnow

Thanks! How on earth did I miss that initially...