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    Solving Matrix Representation: Linear Transformation

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    Let T be a linear operator on P_3 defined as follows:
    T(ax^3 + bx^2 + cx + d) = (a - b)x^2 + (c - d)x + (a + b - c).
    The matrix [T]_G which represents T with respect to the basis G which = {1 + x, 1 - x, 1 - x^2, 1 - x^3}. Show that the standard matrix representation and the preceding matrix representation are similar. Show work.

    © BrainMass Inc. brainmass.com October 9, 2019, 3:46 pm ad1c9bdddf
    https://brainmass.com/math/linear-transformation/solving-matrix-representation-linear-transformation-12941

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    ** Please see the attached file for the full solution **

    1. Let T be a linear operator on P_3 defined as follows:
    T(ax^3 + bx^2 + cx + d) = (a - b)x^2 + (c - d)x + (a + b - c).
    The matrix [T]_G which represents T with respect to the basis G which = {1 + x, 1 - x, 1 - x^2, 1 - x^3}. Show that the standard matrix representation and the preceding matrix representation are similar. Show work.

    Well, here we have to find the standard matrix first:
    {1,x,x^2,x^3} ...

    Solution Summary

    This solution details the concept of matrices in a very detailed, step-wise response that is provided within an attached Word document.

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