Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² + 3t³ + t², 1+t+21² + 3t³ + 2t¹} (a)!'. Write the coordinate vector of each polynomial in S in terms of the standard basis for P4. (b) ;) Determine whether the vectors in S are linearly independent in P4? Do they span P₁?

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