Page 332 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

(b) Consider the operation on that takes to . Does it correspond to a linear
transformation from to ? If so, what is its matrix?

3. in to in . Show that it does not correspond to a linear
(a) Consider the transformation of

transformation by showing that there is no matrix that maps in to in R.

(b) Does the transformation of in to a in correspond to a linear transformation from to R?

4. that takes in to in . Does this correspond to a linear
(a) Consider the operation

transformation from to ? If so, what is its matrix?

(b) Consider the operation that takes in to in . Does this correspond to a linear

transformation from to ? If so, what is its matrix?

(c) Consider the operation that takes in to in . Does this correspond to a linear

transformation from to ? If so, what is its matrix?

5. (For Readers Who Have Studied Calculus) What matrix corresponds to differentiation in each case?
(a)
(b)
(c)

6. (For Readers Who Have Studied Calculus) What matrix corresponds to differentiation in each case, assuming we represent

as the vector ?

Note This is the opposite of the ordering of coefficients we have been using.

(a)
(b)
(c)