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

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1. Feb 20, 2015

### Candice

1. The problem statement, all variables and given/known data
1. What is the relation between the image of A and the image of A2 + A?
2. Relevant equations

3. 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

2. Feb 20, 2015

### PeroK

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.