Page 302 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

is a rotation.
(b) Find a vector of length 1 that defines an axis for the rotation.
(c) Use the result in Exercise 27 to find the angle of rotation about the axis obtained in part (b).

In words, describe the geometric effect of multiplying a vector x by the matrix A.
29.

(a)

(b)

In words, describe the geometric effect of multiplying a vector x by the matrix A.
30.

(a)

(b)

In words, describe the geometric effect of multiplying a vector x by the matrix
31.

If multiplication by A rotates a vector x in the -plane through an angle , what is the effect of
32. multiplying x by ? Explain your reasoning.

Let be a nonzero column vector in , and suppose that is the transformation

33. defined by , where is the standard matrix of the rotation of about the origin

through the angle . Give a geometric description of this transformation. Is it a linear
transformation? Explain.

A function of the form is commonly called a “linear function” because the graph

34. of is a line. Is f a linear transformation on R?

Let be a line in , and let be a linear operator on . What kind of

35. geometric object is the image of this line under the operator T? Explain your reasoning.