Let a be an sxn matrix and B be an mxn matrix composed of the first m rows of A. It is proved that if the rank of the row vector group of a is r, then R (b) > = R + m-s

Let a be an sxn matrix and B be an mxn matrix composed of the first m rows of A. It is proved that if the rank of the row vector group of a is r, then R (b) > = R + m-s

Proof: let a's row vector group be A1, A2,..., am,..., as
Then the row vector group of B is A1, A2,..., am
The rank of row vector group of a is r, that is R (a) = R
It is proved that R (b) > = R (a) + m-s
Let Ai1, AI2,..., air (b) be maximal independent groups of A1, A2,..., am
Then it can be extended to the maximal independent group of A1, A2,..., am,..., as (that is, the maximal independent group of row vector group of a)
But it can only be expanded from the S-M vectors a (M + 1),..., as
So r (a) = R + m-s