Denoting by PN the vector space of polynomials of degree less than or equal to N, with real coefficients, let T : P1 → P2 be defined by T(ax + b) = (x + λ)(ax + b), where λ = 8. Considering β1 = {2, x − 1}, base of P1 and β2 = {1,x, x2}, basis of P2, construct the matrix [T]β1β2, of the transformation T with respect to these bases, and determine dim(Im(T)).

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