Question: Prove is an eigenvalue of A and find a basis for it's space.

Solution: (My friend gave a different answer so I'd like to know which one is correct)

if matrix A is singular. Matrix A is clearly singular...

To find a basis, I do the elementary operations on matrix A and I'm left with

Matrix A has a rank of 1 ---- dimp=n-p(A) ---- dimp = n-1

.

.

.

+ +...+

and those eigenvectors form the basis for that space.

My friend got:

, ,...,

So which is the correct answer? (or is it possible they are both correct...or incorrect)