1. Not finding help here? Sign up for a free 30min 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!

Linear Algebra proof

  1. Sep 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Let A be a nxn matrix, and I the corresponding identity matrix, both in the real numbers ℝ. Assume that A^m=0 for a positive integer m. Show that I-A is an invertible matrix.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 15, 2013 #2

    lurflurf

    User Avatar
    Homework Helper

    Hint what is

    $$\sum_{j=0}^m \, A^j$$

    what is

    $$(I-A)\sum_{j=0}^m \, A^j$$
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Linear Algebra proof
  1. Linear Algebra Proof (Replies: 8)

  2. Linear Algebra proof (Replies: 21)

Loading...