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Let P3 be the vector space of polynomials of degree at most 3 and let B = 1, t, t^2, t^3 be the standard basis for P3. Consider € = p1 (t), p2 (t), ps (t) where p1 (t) = 1 - t^2, p2 (t) = 3 2t, ps (t) = 1 2t - t^2.i) Find [p1 (t)]B, [p2 (t)]B, and [ps (t)]B.ii) Show that € is linearly independent in P3, but it is not a basis for P3.
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