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!

Rank, Co-factor matrices.

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data

    Let A be an n x n matrix where [itex]n \geq 2[/itex]. Show that [itex]A^{\alpha} = 0[/itex] (where [itex]A^{\alpha}[/itex] is the cofactor matrix and 0 here denotes the zero matrix, whose entries are the number 0) if and only if [itex]rankA \leq n-2[/itex]

    2. Relevant equations

    3. The attempt at a solution
    No idea where to start with this, it's just an additional question in the lecture notes which I haven't gone through in tutorial. Thanks.
  2. jcsd
  3. Apr 1, 2012 #2
    The cofactor matrix is obtained by deleting rows and columns and taking the determinant. Given the rank<=n-2, what about the rank after deletion? What about the determinant?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Rank, Co-factor matrices.
  1. Rank of two matrices (Replies: 0)