Friday, 29 January 2016

linear algebra - Let A and B be two 3×3 matrices with real entries such that rank(A)=rank(B)=1.

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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