Consider the polynomials p 1 (t) 1 t, P 2 (t) 1 t P 3 (t) 4 P 4 (t) t t 2 , P 5 (t) 1 2t t 2 and let H be the subspace of P 5 spanned by the set S P 1 , P 2 , P 3 , P 4 , P 5 ) Use the method described in the proof of the Spanning Set Theorem to produce a basis for H (Explain how to select appropri...

The vector p 1 is not zero and p 2 is not a multiple of p 1 However p 3 is 2p 1 2p ...

Consider the polynomials p 1 (t) = 1 + t, P 2 (t) =1 - t P

Question:

Consider the polynomials p₁(t) = 1 + t, P₂ (t) =1 - t P₃(t) = 4 P₄(t) = t + t², P₅ (t) = 1 + 2t + t². and let H be the subspace of P⁵ spanned by the set S = {P₁, P₂, P₃, P₄, P₅). Use the method described in the proof of the Spanning Set Theorem to produce a basis for H. (Explain how to select appropriate members of S.)