Do you understand that there are an infinite number of answers? If the "eigenspace" can be spanned by a single vector, then there cannot be two independent eigenvectors- and that means, in turn, that there cannot be two distinct eigenvalues. But since you are not given the single eigenvalue, it can be anything. And if a 2 by 2 matrix has only a one independent eigenvector, it is similar to a "Jordan Normal Form"
\begin{bmatrix} a & 1 \\ 0 & a\end{bmatrix}
where a is the eigenvalue.
Then you can construct a matrix, P, having the given eigenvector <2, 1>, as first column, and just choose a second row that it easy to find the inverse of P.
Then P^{-1}AP will be a matrix having that only multiples of <2, 1> as eigenvectors. Even after you have done that, you will be able to choosed a to be whatever you want.
