1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Rank of Product Of Matrices

  1. Nov 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Let A be an m * n matrix with rank m and B be an n * p matrix with rank n. Determine the rank of AB. Justify your answer.

    2. Relevant equations

    3. The attempt at a solution

    I don't really know where to start off, but I have some things that might help me. I know that the rank of a matrix is equal to the number of linearly independent rows in it, and I also know that if A and B are two matrices, then rank(AB) <= rank(A) and also rank(AB) <= rank(B).

    I'm sure if I was given a push in the right direction I could solve this.
  2. jcsd
  3. Nov 18, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    What's the relation between the rank of a matrix and the dimension of the image?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook