Let K be a field n e N. Suppose the vector space Pn K[x] with...

 

 

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Let K be a field n e N. Suppose the vector space Pn ≤ K[x] with a basis of Bn = {1, x, x2,...,xn). Let a0, a1,..., an € K with ai unequal to aj. The function is defined as : Pn → Kn+1, f→ (f(a0), f(a1), ... f(an)). Find for the elements a0, a1, a2, a3 the transformation matrix A BS4 with basis B3 of P3 and S4 as the standard basis of K4. f(ao)\ ƒ (a1) Φ: Pn → Kn+1, f→ f(an)) Let K be a field n e N. Suppose the vector space Pn ≤ K[x] with a basis of Bn = {1, x, x2,...,xn). Let a0, a1,..., an € K with ai unequal to aj. The function is defined as : Pn → Kn+1, f→ (f(a0), f(a1), ... f(an)). Find for the elements a0, a1, a2, a3 the transformation matrix A BS4 with basis B3 of P3 and S4 as the standard basis of K4. f(ao)\ ƒ (a1) Φ: Pn → Kn+1, f→ f(an))