Let A and B be two 3×3 matrices with real entries such that rank(A)=rank(B)=1. Let N(A) and R(A) stand for the null space and range space of A. Define N(B) and R(B) similarly. Then which of the following is necessarily true ?
(A)dim(N(A)∩N(B))≥1.
(B)dim(N(A)∩R(A))≥1.
(C)dim(R(A)∩R(B))≥1.
(D)dim(N(B)∩R(B))≥1.
I am feeling that option A is true..Can anyone help me in this..
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