Finding corresponding eigenvalues to a set of eigenvector
Think about the definition of an eigenvector. An eigenvector v of a linear transformation represented by matrix A is a vector that only changes in magnitude, not direction, when that linear transformation is applied to it. The scalar change in magnitude of the eigenvector is its eigenvalue. You have a linear transformation, and you've been given its eigenvectors - to find the eigenvalues, all you need to do is apply the transformation to the eigenvectors and determine by what scalar each eigenvector got scaled.
I solved most of this assignment using Python, but not sure how to input (or even understand) the remaining information. Aren't you supposed to find the eigenvector given some eigenvalue, thus it appears in reverse in the following: 
Let the symmetric 3 × 3 matrix A be A = ((1 2 1), (2 5 0), (1 0 5))
If A has the following three eigenvectors, then find three corresponding eigenvalues:
v1 = ((-5), (2), (1)); v2 = ((0), (-1), (2)); v3 = ((1), (2), (1))