1. In each part below, how many linear transformationsTare there that satisfy the given properties? (Of course, justify your answer!). Write complete solution in legible handwriting and do not skip steps.

(a)T:R3P3(R),T((1,0,0)) =xx2,T((1,1,0)) =x2x3,T((1,1,1)) =xx3

(b)T:R2P3(R),T((1,0)) =xx2,T((1,1)) =x2x3,T((1,2)) =xx3

(c)T:P1(R)P3(R),T(1) =xx2,T(x+1) =x2x3,T(2x+1) =x+3x22x3