Question

Let B be an m x p matrix and let C be a p x n matrix. Prove that the rank of the m x n matrix A=BC satisfies
rank(A)<=min{rank(B), rank(C)}.

Answer 1

@helder_edwin could you please take a look at this problem when you get a chance.

Answer 2

There was a question just like this in the MIT Linear Algebra section. I replied to it, here's the link:

http://openstudy.com/study#/updates/508acb4de4b077c2ef2e515d

Use the Fundamental Theorem of Linear Algebra and the properties of column space to get your proof.

Answer 3

Thank you for your guidance, I will definitely see if I can figure that out once I finish these last two problems.