(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: Nilpotent matrix wit h index 2

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