Question: In the given problem, A is an n x n (square) matrix.  Mark each statement True or False. Explain your answer.

1. If Ax = lambda x for some vector x, then lambda is an eigenvalue of A.
2. Finding an eigenvector of A may be difficult, but checking whether a given vector is in fact an eigenvector is easy.
3. To find the eigenvalues of A, reduce A to echelon form.
4. A number c is an eigenvalue of A if & only if the equation (A - cI)x = 0 has a non-trivial solution
5. A matrix A is not invertible if & only if 0 is an eigenvalue of A.