Question: 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

  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

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