Consider the linear transformation T : P2(R) → M2x2(R) defined by ао + 2а2 ao – 3a1 T(a2x² + a1x + ao) |4ao 4ао — 12a1 2ao + 4a2 - Find the matrix for T, [T], where [1 0] To 1 B = {1, x, x²} C = 0 0 1 0 are bases for P2(R) and M2×2(R) respectively. Find bases for Ker(T) and Rng(T). Is T one-to-one, onto, neither, or both?

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