(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that A is a 6x6 matrix with real values and has a min. poly of p(s) = s^3.

a) Find the Characteristic polynomial of A

b) What are the possibilities for the Jordan form of A?

c) What are the possibilities of the rank of A?

2. Relevant equations

See below.

3. The attempt at a solution

a) I only see that 3 of the eigenvalues are zero, but dont know how to find the rest for the characterisitic polynomial

b) The Jordan blocks can be size 1,2, or 3 i.e. [L 1 0; 0 L 1; 0 0 L], [L 0 0; 0 L 0; 0 0 L], [L 1 0; 0 L 0; 0 0 L] where L are the eigenvalues from the min. poly. (equal to zero)

c) rank(A) + dim N(A) = n, where N(A) is the nullspace of A, and n = 6. Do I just need to find the nullspace of A (and if so, how?) or am I going down the wrong direction.

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# Homework Help: Minimal Polynomial and Jordan Form

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