2. (Verifying solutions.)

8.
(Is a set of 3 vectors a basis for the solution space?)
Verify that each of the 3 vectors **is** a solution.
You need to show that the 3 vectors are LI.

18. (Find the general solution of a non-homogeneous difference equation.)

HINT: See hint for Exercise 17!

X.
Find a stochastic matrix *P* with non-negative entries at least one of which is zero,
for which all the entries of *P*^{k} are strictly positive for some k.
In other words, find a *regular stochastic matrix* with a zero in it.
Explicitly show that it is regular.

32. (An eigenvalue/vector of a rotation about a line through origin.)

16. (Eigenvalues and multiplicities for a diagonal matrix.)

22. (True/False and why.)

23. (RQ for A=QR.)

2.
(*A*^{4} from P,D.)

6. (Eigenvalues and bases for eigenspaces from diagonalization.)

22. (True/False and why.)