Define linear transformations S P1 P2 and T P2 P1 by S(a bx) a (a b )x 2bx2 and T(a bx cx2) b 2cx Compute (S T) (3 2x x2) and (S T) (a bx cx2) Can you compute (T S) (a bx) If so, compute it

Question: Define linear transformations S: P1 P2 and T: P2 P1 by S(a + bx) = a + (a + b )x + 2bx2

Define linear transformations S: P1 → P2 and
T: P2 → P1 by
S(a + bx) = a + (a + b )x + 2bx2
and T(a + bx + cx2) = b + 2cx
Compute (S ͦ T) (3 + 2x - x2) and
(S ͦ T) (a + bx + cx2). Can you compute
(T ͦ S) (a + bx)? If so, compute it.

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