The linear transformation L: P2 (R) → P3 (R) is defined by L(p(x)) = xp(x). Find the matrix [L] B,S where S = {1, x, x²} is the standard basis for P2 (R) and B = {1x, 1+x, x², x³} is a basis for P3(R). Is the transformation 1-1? onto?

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