Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download
3774 views
ubuntu2004
Tweet
Share
Share
1
<?xml version='1.0' encoding='UTF-8'?>

2
<exercise xmlns="https://spatext.clontz.org" version="0.0">

3
  <statement>

4
    <p>

5
        Consider the following maps of polynomials <m>S:\mathcal{P}\rightarrow\mathcal{P}</m>

6
        and <m>T:\mathcal{P}\rightarrow\mathcal{P}</m> defined by

7
        <me>

8
            S({{f_letter}}(x))=

9
                {{#swapped}}

10
                    {{nonlinear_trans}}

11
                {{/swapped}}

12
                {{^swapped}}

13
                    {{linear_trans}}

14
                {{/swapped}}

15
                \hspace{1em} \text{and} \hspace{1em}

16
            T({{f_letter}}(x))=

17
                {{^swapped}}

18
                    {{nonlinear_trans}}

19
                {{/swapped}}

20
                {{#swapped}}

21
                    {{linear_trans}}

22
                {{/swapped}}

23
        </me>

24
        Explain why one these maps is a linear transformation and why the other map is not.

25
    </p>

26
  </statement>

27
  <answer>

28
      {{#swapped}}

29
            <p><m>S</m> is not linear and <m>T</m> is linear.</p>

30
      {{/swapped}}

31
      {{^swapped}}

32
            <p><m>S</m> is linear and <m>T</m> is not linear.</p>

33
      {{/swapped}}

34
  </answer>

35
</exercise>

36