Page 658 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(b) Find the rank and nullity of T.

Suppose that vectors in are denoted by matrices, and define by
6.

(a) Find a basis for the kernel of T.
(b) Find a basis for the range of T.

Let be a basis for a vector space V, and let be the linear operator for which
7.

(a) Find the rank and nullity of T.
(b) Determine whether T is one-to-one.

Let V and W be vector spaces, let T, , and be linear transformations from V to W, and let k be a scalar. Define new

8. transformations, and , by the formulas

(a) Show that and are linear transformations.

(b) Show that the set of all linear transformations from V to W with the operations in part (a) forms a vector space.