Abstract: Let B_n be the set of all n×n Boolean Matrices;R(A) denote the row space of A∈B_n,|R(A)| denote the cardinality of R(A),m,n,k,l,t,i,γi be positive integers,Si,λi be non negative integers.In this paper,we prove the following two results: (1)Let n≥13,n-3≥k > S_l,S_i+1> S_i,i = 1,2,…,l-1.if k+l≤n,then for any m=2k+2(S_l) + 2(S_l-1)+…+ 2(S₁),there exists A∈B_n,such that |R(A)|= m. (2)Let n≥13,n-3≥k>S_n-k-1> S_n-k-2>…>S₁>λ_t>λ_t-1>…>λ₁,2≤t≤n-k.If exist γ_i(k+1≤γ_i≤n-1,i=1,2,…,t-1)γ_i<γ_i+1 and λ_t-λ_t-1≤k-S(_n-γ1),λ_t-i-λ_t-i-1≤S(_n-γi)-S(_n-γi+1),i=1,2,…,t-2,then for any m=2^k+2(^SN-K-1)+2(^Sn-k-2)+…+2(^S1)+2(^λt)+2(^λt-1)+…+2(λ1),there exists A∈Bn,as such that |R(A)|=m. 

Key words:  Boolean ,  matrix; ,  row ,  space; ,  cardinality ,  of , a ,  row ,  space