Is there a linear map T : P2(R) ->R2 such that T(1) = (2, 3), T(1+x) = (-2, 7), and T(1+x+x^2) =
(0, 9)? Justify your answer.
1
Expert's answer
2020-11-08T19:44:20-0500
Clearly 1,1+x,1+x+x2 forms a basis of P2(R). This follows from the fact that x=1+x−1,x2=1+x+x2−1−(1+x) and 1,x,x2 forms a basis. Now mapping any basis to any set of vectors gives a linear map. Hence the given map is linear. We need to extend the map by linearity on the entire space.
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