Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Construct a 2x2 matrix that is not the zero vector

  1. Oct 12, 2007 #1
    Construct a 2x2 matrix that is not the zero vector yet satisfies A^2=0 been studying this question for a while...any help?
    Last edited: Oct 12, 2007
  2. jcsd
  3. Oct 12, 2007 #2
    Do you mean A is a 2x2 matrix which is not a zero matrix, and it is such that A^2 = 0 ?
  4. Oct 12, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    a) think geometrically


    b) think in terms of basis vectors


    c) just do it - write out a general a,b,c,d matrix square it and see what choices of a,b,c,d would mean its square is 0.
  5. Oct 19, 2007 #4
    Look up nilpotence too, wont help you solve the question but its interesting and related to it :)
  6. Oct 19, 2007 #5


    User Avatar
    Science Advisor

    Or even, just write out a matrix

    [a b]
    [c d], square it and see what equations must be satisfied to be the 0 vector!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook