Question

(6) Label each of the following statements as True or False. Provide justification
for your response.

(b) True/False The scalar λ is an eigenvalue of a square matrix A if and
only if the equation (A − λIn)x = 0 has a nontrivial solution.
(c) True/False If λ is an eigenvalue of a matrix A, then there is only
one nonzero vector v with Av = λv.
(d) True/False The eigenspace of an eigenvalue of an n × n matrix A
is the same as Nul (A − λIn).
(f) True/False If v1 and v2 are eigenvectors of a matrix A, then v1+v2
is also an eigenvector of A.

Answer 1