Page 660 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Show that the matrices
16.

are similar but that

are not. is a linear operator and B is a basis for V such that for any vector x in V,

Suppose that
17.

Find . .
be a linear operator. Prove that T is one-to-one if and only if
Let
18.

19. (For Readers Who Have Studied Calculus)

(a) Show that if , then the function defined by is a
form a two-dimensional subspace of
linear transformation.

(b) Find a basis for the kernel of D.

(c) Show that the functions satisfying the equation
, and find a basis for this subspace.

Let be the function defined by the formula
20.

(a) Find .

(b) Show that T is a linear transformation.
(c) Show that T is one-to-one.