Please help. What is the relation between the kernel of A an

[Candice]

Homework Statement

1. What is the relation between the kernel of A and the kernel of (A^2 + A)?

Homework Equations

The Attempt at a Solution

Break into A^2x = 0 and Ax = 0. We know Ax = 0 because that's the kernel of A, ker(A^2x) is subset of ker(A) so ker(A^2 + A) is a subset of ker (A)?

 

[PeroK]

Homework Statement

1. What is the relation between the kernel of A and the kernel of (A^2 + A)?

Homework Equations

The Attempt at a Solution

Break into A^2x = 0 and Ax = 0. We know Ax = 0 because that's the kernel of A, ker(A^2x) is subset of ker(A) so ker(A^2 + A) is a subset of ker (A)?

Why not start with $x \in ker(A)$ and start from there? You need to formalise your answer. You've got an outline for the answer, but you need to sharpen your logic.

 

[HallsofIvy]

In both this and the previous question about image, it is useful to note that $A^2+ A= A(A+ I)= (A+ I)A$.