# 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.

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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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** 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} ...

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