Consider linear transformation T: M22 → P3 defined by T ([ª d]) = (a + b)2²³ + (b + c)2² + (c + d)x + (d + a). (a) Find a basis of ker T and a basis of im T. (b) Let S : P3 → R be the linear transformation defined as S(p(x)) = p(0). Find a basis of ker(SoT) and show that SoT is onto.

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