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Linear algebra, I need someone to tell me how to get T(1)=1,1,1 T(x)=-1,0,1 T(x^2)=1,0,1 T(x^3)=-1,0, 1 I don't have any clue to find this. please follwo the comment

WHAT FORMULA SHOULD I PLUG IN WHEN I PLUG IN T(1), T(X)......

How about this: Problem 2. Let P3 = Span {1,2,22,23 , the vector space of polynomials with degree at most 3, and let T : P3 → R3 be the linear transformation given by T(p)p(0) 1000 1) Find the matrix representing T relative to the bases B{1, z, 2,3 and D (ei, e2,es)- 2) Determine ker(T), the kemel of T Solution TB = {T( 1), T (z), T (t) , T (-)) 1-1 1-1 - ei, e2, e31 0 0 0 DTDs Thus, TIp1 o o o

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