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decoding matrix

Hi, I am stuck on reducing the following matrix. It is supposed to be in H = CI format where C = Coding matrix and I = Identity matrix

1 1 1 1 1
1 2 3 4 0

and its a mod 5 matrix

I am wondering if anyone could help me reduce the above matrix to following format using row operations

* * * 1 0
* * * 0 1

Many Thanks
Can you do swapping? it so swap row 1 and 2 to get
1 2 3 4 0
1 1 1 1 1

R1 -> R1 - 3*R2
R2 -> R2 - R1

That should get you a
1 0
0 1
in the last two columns

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