Rank of two matrices

  • #1

Homework Statement



A is nxn
B is nxp

Is the rank of

[B AB ... An-1B]

equal to the rank of

[AB A2B ... AnB]?

If not, under what condition will the ranks be equal?

The Attempt at a Solution



I don't even know where to start. I know that both matrices should have the same number of pivots, but since this is so generalized I don't know how to learn anything about how multiplying by A would change the number of pivots!

Can someone help me out and at least give me a hint? I've been staring at this for the longest time and just don't know what to do!

Thanks!
 

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