Page 648 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

In each part, find a basis for relative to which the matrix for T is diagonal.
12.

(a)

(b)

(c)

Let be defined by
13.

(a) Find the eigenvalues of T.
(b) Find bases for the eigenspaces of T.

Let be defined by
14.

(a) Find the eigenvalues of T.
(b) Find bases for the eigenspaces of T.

Let λ be an eigenvalue of a linear operator . Prove that the eigenvectors of T corresponding to λ are the nonzero

15. vectors in the kernel of .

16.
(a) Prove that if A and B are similar matrices, then and are also similar. More generally, prove that and are
similar, where k is any positive integer.

(b) If and are similar, must A and B be similar?

Let C and D be matrices, and let be a basis for a vector space V. Show that if
17.