You can use the unique function:
unique(mat$V1) # and not matrix$v1
[1] 44 281 1312
You can also write
unique(mat)
and it will give you unique lines (I tried it on your file).
If you want to select on V1s values, you can do this:
> mat[!duplicated(mat$V1), ]
X V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
1 1547 44 14 1 2 100 17 0 0 0 0
23 5385 281 67 2 10 100 10 0 0 0 0
33 17347 1312 1 2 6 100 8 0 0 0 0