Let B = {1,1+x,1+ x + x² }. (a) Check whether that the set B is a basis for P2. 2 (b) Let p(x) = 1+3x +x². Compute the coordinate [p(x)]g of p(x).

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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A: Solution is in explanatio area.Explanation:

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Q: Extend {1 + x, 1 + x + x2} to a basis for P3.

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Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

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Q: (5) Let T P₂ → P₁ represented by T(ao + a₁ + a₂x²) = a₁ + 2a₂x. Find kernel of T.

A: We have to find kernel of T.