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  3. consider the vector space p2 := p2(f) and its stan

Consider the vector space P2 := P2(F) and its standard basis ? = {1,x,x^2}. 1Prove that ?...

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Advance Math

Consider the vector space P2 := P2(F) andits standard basis ? = {1,x,x^2}.

1Prove that ? = {x?1,x^2 ?x,x^2 + x} is also a basis ofP2

2Given the map T : P2 ? P2 de?ned by T(a + bx + cx2) = (a + b +c) + (a + 2b + c)x + (b + c)x2
compute [T]??.

3 Is T invertible? Why

4 Suppose the linear map U : P2 ? P2 has the matrixrepresentation

(1 0 0

0 2 0

0 0 4)

Compute [UT]?? and complete the followingformula
(UT)(a+bx+cx2) =

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