Let A
=
(
4
−
1
2
1
)
(a) Verify the Cayley-Hamilton theorem for A
.
(b) Find the eigenvalues of A
.
(c) For each eigenvalue of A
, determine an eigenvector.
(d) Find a diagonal matrix D
and an invertible matrix P
such that A
=
P
D
P
−
1
.
(e) Compute A
10
.