Linear algebra find the minimal polynomial

[catsarebad]

Homework Statement

M: V -> V linear operator st M^2 + 1_v = 0
find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v

Homework Equations

The Attempt at a Solution

using M^2 = -1_v,
i rewrote the operator(?) as
M^3 + M + I_v

i don't know what to do. i guessed min poly to be like x^3-x-1
but what would be other possibilities. i seriously doubt the one i guessed is even correct.

i know that, if min poly is u(x) then u(M) = 0.

 

[Dick]

Homework Statement

M: V -> V linear operator st M^2 + 1_v = 0
find the POSSIBILITIES for min. pol. of M^3+2M^2+M+3I_v

Homework Equations

The Attempt at a Solution

using M^2 = -1_v,
i rewrote the operator(?) as
M^3 + M + I_v

i don't know what to do. i guessed min poly to be like x^3-x-1
but what would be other possibilities. i seriously doubt the one i guessed is even correct.

i know that, if min poly is u(x) then u(M) = 0.

M^3=(-M), isn't it?

 

[catsarebad]

got it.