Define For instance, if a. Show that T is a linear

Chapter 4, Problem 31E

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QUESTION:

Problem 31E

Define  For instance, if

a. Show that T is a linear transformation. [Hint: For arbitrary polynomials p, q in , compute

b. Find a polynomial p in  that spans the kernel of T , and describe the range of T .

Questions & Answers

QUESTION:

Problem 31E

Define  For instance, if

a. Show that T is a linear transformation. [Hint: For arbitrary polynomials p, q in , compute

b. Find a polynomial p in  that spans the kernel of T , and describe the range of T .

ANSWER:

Solution 31E

Step 1 of 4

Consider that the mapping  defined by .

(a) The objective is to show that T is a linear transformation.

Consider the arbitrary polynomials  in.

Let c be any scalar.

To find:

Therefore, is closed under vector addition.

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