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Change of Basis : Matrix Representation

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Let E= {1, x, x^2, x^3} be the standard ordered basis for the space P_3. G= {1+x, 1-x, 1-x^2, 1-x^3} is also a basis for P_3. Write the matrix representation [p(x)]_G for the polynomial (vector) p(x)=3x^3-2x+4 from P_3 with respect to the basis G. Show work.

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In this solution a matrix representation of a vector is shown in respect to a basis. The solution is detailed and well presented.

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