Is k an Eigenvalue of A with Sum of Row Entries as k?

[mjthiry]

1. Homework Statement

Suppose that A is a square matrix and the sum of the entries of each row is some number k. Is k an eigenvalue of A? if so, what is the corresponding Eigenvector?2. Homework Equations

Ax-λx=0
3. The Attempt at a Solution

(1-k)(K-λ)-k=0I am not sure how to solve this in a proof sense ( since we are not using specific numbers)

 

[vela]

Is there a vector can you multiply into A where the product will be (k, k, k, ..., k)^T?