Compute the expansion coefficients of 2-tuple [3, 2]T for the following bases and write th...

Compute the expansion coefficients of 2-tuple [3, 2]T for the following bases and write the corresponding expansions:

(a) Basis and on R2 , the set of real 2-tuples.

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(b) Basis φ0 = [1, 0]T and φ1 = [1, 1]T, and its dual, and

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(c) Basis and and their duals, for i = {0, 1, 2,}, on R2.

(Hint: Vector inner products must be used in place of the integral inner products of Section 7.2.1.)