Finding Eigenvectors with a Parameter in Homework Solution?

[Maybe_Memorie]

Homework Statement

Okay, we've got a 3x3 matrix. All the entries are equal to 1. Call the matrix A.
Basically It looks like this
1 1 1
1 1 1
1 1 1

find all the eigenvalues and eigenvectors.

The Attempt at a Solution

Right, I got the eigenvalues being 0 and 3, the same as my lecturer got. That's fine, I just let the determinant of (\lambdaI-A) equal 0.
When getting the eigenvectors, every book I read gives the vector in terms of a parameter, such as t. However, my lecturer got vectors with specific coordinates.

What am I supposed to do?

 

[Robert1986]

Homework Statement

Okay, we've got a 3x3 matrix. All the entries are equal to 1. Call the matrix A.
Basically It looks like this
1 1 1
1 1 1
1 1 1

find all the eigenvalues and eigenvectors.

The Attempt at a Solution

Right, I got the eigenvalues being 0 and 3, the same as my lecturer got. That's fine, I just let the determinant of (\lambdaI-A) equal 0.
When getting the eigenvectors, every book I read gives the vector in terms of a parameter, such as t. However, my lecturer got vectors with specific coordinates.

What am I supposed to do?

Let v be an eigenvector of your matrix and let l be its eigenvalue. If A is your matrix then, as you know Av = lv. Now, what if you were to take a multiple of v, is that an eigenvector? That is, if k is a scalar, is kv an eigenvector? If so, can you think of a parametrized form of v that would include all multiples of v?