Rank of Product Of Matrices

  • Thread starter JG89
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Homework Statement



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.





Homework Equations





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.
 

Answers and Replies

  • #2
Dick
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What's the relation between the rank of a matrix and the dimension of the image?
 

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