P5: Compute the characteristic polynomial, eigenvalues and the dimensions of the eigenspaces for the

3 3 matrix A, where A = I 2 n n T and n R3 is a unit (column) vector.

Hint: Perhaps try computing eigenvectors first, and deducing the eigenvalues and characteristic poly-

nomial later? Alternatively, give a geometric interpretation of A and use that to deduce eigenvalues and eigenvectors.