Given that the matrices $A,B:\mathbb{R}^{17}\to\mathbb{R}^5$ with full row rank =$5$= collumn rank, it is easy to see that both has kernel dimension $12$, now my question is what can I say about common solution space of the equations involved with this two matrix A,B as follows: $Ax=0$ and $Bx=0$
Well, (1) they may have identical kernel i.e $\dim(\ker(A)\cap\ker(B))=12$
(2) Can It be possible $\dim(\ker(A)\cap\ker(B))=11,10,9,\dots,1$? I think not since they have full row rank?
(3) If, $Ax=0$ has non trivial solution then its column vectors are linearly dependent or row vectors are linearly dependent?
thanks for helping