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, 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook