A is an n\times n matrix. check the true statements below:

a. an eigenspace of a is just a null space of a certain matrix.

b. if v_{1} and v_{2} are linearly independent eigenvectors, then they correspond to distinct eigenvalues.

c. if ax = \lambda x for some nonzero vector x, then \lambda is an eigenvalue of

a.

d. if ax = \lambda x for some vector x, then x is an eigenvector of

a.

e. the eigenvalues of a matrix are on its main diagonal.