Page 807 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(f)

Show that if v is a nonzero vector in , then has Euclidean norm 1.
7. .

Find all scalars k such that , where
8.

Find the Euclidean inner product if
9.

(a) ,

(b) ,

(c) ,

In Exercises 10 and 11 a set of objects is given, together with operations of addition and scalar multiplication. Determine
which sets are complex vector spaces under the given operations. For those that are not, list all axioms that fail to hold.

The set of all triples of complex numbers with the operations
10.

and

The set of all complex matrices of the form
11.

with the standard matrix operations of addition and scalar multiplication.

Use Theorem 5.2.1 to determine which of the following sets are subspaces of :
12.

(a) all vectors of the form

(b) all vectors of the form

(c) all vectors of the form , where

(d) all vectors of the form , where

Let T: be a linear operator defined by , where
13.