Page 601 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Find a basis for the kernel of
7.

(a) the linear operator in Exercise 1
(b) the linear transformation in Exercise 3
(c) the linear transformation in Exercise 5.

Find a basis for the range of
8.

(a) the linear operator in Exercise 1
(b) the linear transformation in Exercise 3
(c) the linear transformation in Exercise 5.

Verify Formula 1 of the dimension theorem for
9.

(a) the linear operator in Exercise 1
(b) the linear transformation in Exercise 3
(c) the linear transformation in Exercise 5.
In Exercises 10–13 let T be multiplication by the matrix A. Find
(a) a basis for the range of T
(b) a basis for the kernel of T
(c) the rank and nullity of T
(d) the rank and nullity of A

10.

11.