Transforming matrix for a linear transformation:












1












$begingroup$



Linear transformation: $T:mathbb{R}[X]_{≤2}rightarrowmathbb{R}^3$



With $T(f):=(f(0), f'(1),f(2))$ and $mathbb{R}[X]_{≤2}$ is the $mathbb{R}$-vector space of the polynomials of degree ≤2



Portray the linear transformation $T$ as matrix referring to the basis $1, X, X^2$ of $mathbb{R}[X]_{≤2}$ and the standard basis of $mathbb{R}^3$




Now I've done the transformation for both the bases, but I don't know if that works:



For the first one I obtain a matrix:



$[1,0,0]$



$[0,1,2]$



$[1,2,4]$



Doing $T(1)=(1,0,1)$, $T(X)=(0,1,2)$, $T(X^2)=(0,2,4)$



And for the standard basis I obtained a matrix:



$[1,0,0]$



$[0,0,0]$



$[0,0,1]$



Doing the same procedure with $T(e_1), T(e_2), T(e_3)$



I'm not sure it's right, and I don't know if I have to get just one another matrix instead of one. Sorry I don't know how to write matrices here...










share|cite|improve this question









$endgroup$

















    1












    $begingroup$



    Linear transformation: $T:mathbb{R}[X]_{≤2}rightarrowmathbb{R}^3$



    With $T(f):=(f(0), f'(1),f(2))$ and $mathbb{R}[X]_{≤2}$ is the $mathbb{R}$-vector space of the polynomials of degree ≤2



    Portray the linear transformation $T$ as matrix referring to the basis $1, X, X^2$ of $mathbb{R}[X]_{≤2}$ and the standard basis of $mathbb{R}^3$




    Now I've done the transformation for both the bases, but I don't know if that works:



    For the first one I obtain a matrix:



    $[1,0,0]$



    $[0,1,2]$



    $[1,2,4]$



    Doing $T(1)=(1,0,1)$, $T(X)=(0,1,2)$, $T(X^2)=(0,2,4)$



    And for the standard basis I obtained a matrix:



    $[1,0,0]$



    $[0,0,0]$



    $[0,0,1]$



    Doing the same procedure with $T(e_1), T(e_2), T(e_3)$



    I'm not sure it's right, and I don't know if I have to get just one another matrix instead of one. Sorry I don't know how to write matrices here...










    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$



      Linear transformation: $T:mathbb{R}[X]_{≤2}rightarrowmathbb{R}^3$



      With $T(f):=(f(0), f'(1),f(2))$ and $mathbb{R}[X]_{≤2}$ is the $mathbb{R}$-vector space of the polynomials of degree ≤2



      Portray the linear transformation $T$ as matrix referring to the basis $1, X, X^2$ of $mathbb{R}[X]_{≤2}$ and the standard basis of $mathbb{R}^3$




      Now I've done the transformation for both the bases, but I don't know if that works:



      For the first one I obtain a matrix:



      $[1,0,0]$



      $[0,1,2]$



      $[1,2,4]$



      Doing $T(1)=(1,0,1)$, $T(X)=(0,1,2)$, $T(X^2)=(0,2,4)$



      And for the standard basis I obtained a matrix:



      $[1,0,0]$



      $[0,0,0]$



      $[0,0,1]$



      Doing the same procedure with $T(e_1), T(e_2), T(e_3)$



      I'm not sure it's right, and I don't know if I have to get just one another matrix instead of one. Sorry I don't know how to write matrices here...










      share|cite|improve this question









      $endgroup$





      Linear transformation: $T:mathbb{R}[X]_{≤2}rightarrowmathbb{R}^3$



      With $T(f):=(f(0), f'(1),f(2))$ and $mathbb{R}[X]_{≤2}$ is the $mathbb{R}$-vector space of the polynomials of degree ≤2



      Portray the linear transformation $T$ as matrix referring to the basis $1, X, X^2$ of $mathbb{R}[X]_{≤2}$ and the standard basis of $mathbb{R}^3$




      Now I've done the transformation for both the bases, but I don't know if that works:



      For the first one I obtain a matrix:



      $[1,0,0]$



      $[0,1,2]$



      $[1,2,4]$



      Doing $T(1)=(1,0,1)$, $T(X)=(0,1,2)$, $T(X^2)=(0,2,4)$



      And for the standard basis I obtained a matrix:



      $[1,0,0]$



      $[0,0,0]$



      $[0,0,1]$



      Doing the same procedure with $T(e_1), T(e_2), T(e_3)$



      I'm not sure it's right, and I don't know if I have to get just one another matrix instead of one. Sorry I don't know how to write matrices here...







      linear-algebra matrices linear-transformations






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Dec 3 '18 at 17:29









      DadaDada

      7510




      7510






















          1 Answer
          1






          active

          oldest

          votes


















          0












          $begingroup$

          There was asked for only one matrix, namely the first one you got.

          Note that writing out the coordinates of a vector in $Bbb R^3$ implicitly uses the standard basis.

          So, we take one basis in the domain (the polynomials), and one in the codomain (the real triples), and ask for the matrix of the transformation with respect to these bases.






          share|cite|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "69"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });














            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024384%2ftransforming-matrix-for-a-linear-transformation%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            0












            $begingroup$

            There was asked for only one matrix, namely the first one you got.

            Note that writing out the coordinates of a vector in $Bbb R^3$ implicitly uses the standard basis.

            So, we take one basis in the domain (the polynomials), and one in the codomain (the real triples), and ask for the matrix of the transformation with respect to these bases.






            share|cite|improve this answer









            $endgroup$


















              0












              $begingroup$

              There was asked for only one matrix, namely the first one you got.

              Note that writing out the coordinates of a vector in $Bbb R^3$ implicitly uses the standard basis.

              So, we take one basis in the domain (the polynomials), and one in the codomain (the real triples), and ask for the matrix of the transformation with respect to these bases.






              share|cite|improve this answer









              $endgroup$
















                0












                0








                0





                $begingroup$

                There was asked for only one matrix, namely the first one you got.

                Note that writing out the coordinates of a vector in $Bbb R^3$ implicitly uses the standard basis.

                So, we take one basis in the domain (the polynomials), and one in the codomain (the real triples), and ask for the matrix of the transformation with respect to these bases.






                share|cite|improve this answer









                $endgroup$



                There was asked for only one matrix, namely the first one you got.

                Note that writing out the coordinates of a vector in $Bbb R^3$ implicitly uses the standard basis.

                So, we take one basis in the domain (the polynomials), and one in the codomain (the real triples), and ask for the matrix of the transformation with respect to these bases.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 3 '18 at 19:07









                BerciBerci

                60k23672




                60k23672






























                    draft saved

                    draft discarded




















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024384%2ftransforming-matrix-for-a-linear-transformation%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Probability when a professor distributes a quiz and homework assignment to a class of n students.

                    Aardman Animations

                    Are they similar matrix