Relation between image(A) and image(A^2+A)

[Candice]

Homework Statement

1. What is the relation between the image of A and the image of A2 + A?

Homework Equations

The Attempt at a Solution

im (A^2 + A) for x (A^2+A) is within the image. Linear combination properties show A^2 x + A x. Not sure where to go from here

 

[PeroK]

Homework Statement

1. What is the relation between the image of A and the image of A2 + A?

Homework Equations

The Attempt at a Solution

im (A^2 + A) for x (A^2+A) is within the image. Linear combination properties show A^2 x + A x. Not sure where to go from here

You need to start formalising your approach. You're really just writing down vague thoughts here!

You are asked to compare two sets. So, start by taking $x \in Im(A)$ and/or $x \in Im(A^2 + A)$ and see what you get.