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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

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    a) think geometrically

    OR

    b) think in terms of basis vectors

    OR

    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

    HallsofIvy

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    Staff Emeritus
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    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!
     
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