# Show transcribed image text Consider P3[0, 1] the linear subspace of C[0,1] consisting of all cubic

linear subspace of C[0,1] consisting of all cubic polynomials. Prove that a sequence {pn” src=”https://files.transtutors.com/questions/transtutors004/images/transtutors004_0b60dd14-11a5-493b-9fb8-ccbc98f248d4.png”>

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Show transcribed image text Consider P3[0, 1] the linear subspace of C[0,1] consisting of all cubic

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Show transcribed image text Consider P3[0, 1] the linear subspace of C[0,1] consisting of all cubic polynomials. Prove that a sequence {pn} where Pn(t) = an0 + an1t + an2t^2 + an3t^3 is convergent in (P3[0,1],I . I infinity) to p where p(t) = a0 + a1t + a2t^2 + a3t^3 if and only if each coefficient sequence {ank} is convergent to ak for each k element of {0,1,2,3}. Consider P[0,1] the li