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Homework Help: Nilpotent matrix wit h index 2

  1. Jun 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Determine a and b such that A is nipotent of index 2.

    A:= <<a,b>|<0,0>>

    A is a 2x2 matrix column 1 is a and b , column 2 is 0's

    2. Relevant equations
    A^k=0 to be nilpotent and to be nipotent it has to be that A^(k-1) doesn't equal 0..

    3. The attempt at a solution
    so far i've tried squaring the matrix and getting a result matrix

    squared:= <<a^2,ba+b^2>|<0,0>>

    so i can only assume that a and b must be zero to insure A^k (in this case k is 2 so squared) but then on A^(2-1) A must not be a zero matrix.. so...

    my class didn't cover nilpotent yet and i guess the teacher just assumed we knew it.. so after doing research thats what i have gotten to understand about it.. but would like some help if someone can point out what i'm missing to make it nilpotent and work on both checks the A^k=0 and A^(k-1) not equal zero

    Yes it is a homework problem, but i did make an attempt at it for 3hrs before asking for help on it, and its not due for a couple days so its not like i'm just saying here solve it for me.. i'm just looking for some help to understand inpontents cause there are some other problems, like 3 on the matter and i just don't get it i guess.
  2. jcsd
  3. Jun 25, 2007 #2


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    Homework Helper

    Unless I'm missing something huge here, you're overcomplicating things. You have a given index (and a "small" one!), and you only have to work one simple matrix equation out (eg matrix is A nilpotent of index 2 if A^2 = 0).
  4. Jun 25, 2007 #3
    but to get it to be nilpotent, a^2=0 and a^(2-1)doesn't eqaul 0, a and b must be given values.. but the only values i've found to work to solve the first part.. proving the second part of the nipotent seems impossible for 2.. because so far a and b being =0 kills the second part of the check
  5. Jun 25, 2007 #4


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    The square of your matrix is <<a^2,b*a>|<0,0>>. Now does b need to be zero?
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