Ariel Pacetti on Fri, 30 Jul 2004 19:10:12 +0200

 Re: Echelon Form

```
May be I wasn't too clear about my question. Let's say I have the matrix:

[0 -1 0 0 0 0 0 0]

[0 -1 0 0 0 0 0 0]

[0 1 -1 0 0 0 1 0]

[0 0 0 1 -1 0 0 1]

[0 0 0 0 1 -1 0 -1]

I want to reduce it so as to get as result:

[0 1 0 0 0 0 0 0]

[0 0 1 0 0 0 -1 0]

[0 0 0 1 -1 0 0 1]

[0 0 0 0 1 -1 0 -1]

[0 0 0 0 0 0 0 0]

```
So what are the "valid" operations? The same as Gaussian elimination, i.e. permute two rows, to a row add a multiple of another one (hence the result may have rational coefficients) and multiply a row by a non-zero constant.
```Note that the answer is not diagonal at all, and may have lots of zeros.
```
May be there is a simpler solution to what I want to do (this does solve it) which is if I have a set of generators of a linear space, how do I get a basis and at the same time a way to write the "extra" elements (the ones that can be removed to get the basis) as a linear combination of the basis? I found that "matimagecompl" answers my first question, but if I get the reduced matrix, I won't need any other computation.
```Cheers,

Ariel

```

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