Here's the question I'm stuck at: Suppose a mapping from R^2 -> R^2 is defined by some 2x2 matrix W. Is the image of W spanned by the eigenvectors of W? Why or why not? 3. The attempt at a solution I know that the eigenvectos of W for a linearly independent set. I also know that the set spanning W will consist of the smallest subspace of W consisting of linear combinations of all vectors in W. But I'm confused about what the eigenvectors actually are. I'm assuming that the answer is "yes", but I don't know why.