Thread: rank of an overdetermined matrix

Hi

I have this matrix that is dimension q x (m + n + 1)
with q much larger than (m + n + 1)
like 88000 x 2096 or about something like that.

It is a binary matrix, all 1s and 0s, but the first column is all 1s.
I have been asked to show that the rank of the matrix is (column rank) is (m + n - 1).
and told that I can make the first column 0 and the last column 0 also, probably becuase of this column rank. i.e. turn it into a 88000 x 2094 matrix.

Can anyone tell me how I would show that this matrix is rank (m + n -1).
Am I to show that the first and last columns are linearly dependent?

Thanks.

The first thing I can think of is that we know the rank has to be less than the dimension.

dim=rank+nullity