Part 2: Let be a real eigenvalue of a matrix with real entries A. Show that the set V = {x : Ax = x} is a subspace of R n . If you reduce your solution to a question about null spaces, be sure to include prove that null spaces are subspaces (but that's fine if you want to do it that way so long as your argument is clear, and correct of course). Hint: check the definition of subspace.

Part 3: Why is the set of eigenvectors of A corresponding to eigenvalue not a subspace? Why does this not contradict what you were asked to do in Part 2? Hint: check the definition of eigenvector.

****Only want answer for part 3, I included part 2 information as a reference*******