Let A and B be two m x n and nx q matrices respectively.
(a) Prove that R(AB) R(A).
(b) Prove that N(B) N(AB).
(c) Deduce that rank AB <min {rank A, rank B}
its hard to read the question like this this is what it lookslike on my homework, i couldnt put in the symbols when i typedit
Let A and B be two m Times n and n Times q matrices respectively. Prove that R(AB) R(A). Prove that N(B) N(AB). Deduce that rank AB min {rank A, rank B}.
