Page 602 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

12.
13.

Describe the kernel and range of
14.

(a) the orthogonal projection on the -plane

(b) the orthogonal projection on the -plane

(c) the orthogonal projection on the plane defined by the equation

Let V be any vector space, and let be defined by .
15.

(a) What is the kernel of T?

(b) What is the range of T?

In each part, use the given information to find the nullity of T.
16.

(a) has rank 3.

(b) has rank 1.

(c) The range of is .

(d) has rank 3.

Let A be a matrix such that has only the trivial solution, and let be multiplication by A. Find the
17. rank and nullity of T.

Let A be a matrix with rank 4.
18.