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Matrix of T(x,y) = (4x - 2y, 2x + y) relative to the basis.

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Let T be a linear map on R^2 defined by T(x,y) = (4x - 2y, 2x + y).
Calculate the matrix of T relative to the basis {α1, α2} where α1 = (1,1) , α2 = (-1,0).

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This solution is comprised of a detailed explanation for finding the matrix of the linear map relative to a basis. It contains step-by-step explanation to find the matrix of T relative to the basis {α1, α2} where α1 = (1,1) , α2 = (-1,0), where T is a linear map on R^2 defined by T(x,y) = (4x - 2y, 2x + y).

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