Page 647 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 647
is the orthogonal projection on the -plane; B and are as in Exercise 4.
5.
is defined by ; B and are the bases in Exercise 2.
6.
is defined by ; and , where ,
,,
7. .
.
Find
8. , where
(a)
(b) , where
(c) , where
Prove that the following are similarity invariants:
9.
(a) rank
(b) nullity
(c) invertibility
Let be the linear operator given by the formula .
10.
(a) Find a matrix for T with respect to some convenient basis; then use Theorem 8.2.2 to find the rank and nullity of T.
(b) Use the result in part (a) to determine whether T is one-to-one.
In each part, find a basis for relative to which the matrix for T is diagonal.
11.
(a)
(b)
