Answer
a) False
b) False
c) True
d) False
e) True
Work Step by Step
a) False. This is only true if the vector x is nonzero
b) False. They may correspond to the same eigenvalue. Then, the eigenvalue will have a multiplicity of greater than 1.
c) True. The steady state means $Ax=x$, which would correspond to an eigenvalue of 1.
d) False. This is only true for triangular matrices
e) True. The eigenspace of A is the null space of $(A-\lambda I)$
