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## Homework Statement

Given the matrix:

0 1 0

0 0 1

12 8 -1

(sorry I don't know how to put proper matrix format)

a) find polynomials a(λ)(λ+2)

^{2}+b(λ)(λ-3) = 1 (where a(λ) and b(λ) are the polynomials)

## The Attempt at a Solution

Well the characteristic polynomial is already given, but can easily be found, as

(λ+2)

^{2}(λ-3)

but how do I find such polynomials? Is this what is meant by the minimal polynomial?