Question: Linear Algebra Consider the polynomial f(x) = 1. Note that the degree of f(r) is less than one so f(r) is in P' (x). We

Linear Algebra

Consider the polynomial f(x) = 1. Note that the degree of f(r) is less than one so f(r) is in P' (x). We have, f(x)p(x) = 1p(x) = 1(ar + b) = ar + b = p(I). So there is a polynomial in Pl(x), f(x) = 1 that acts as an identity element. We have shown P(x) meets all the requirements and therefore is a vector space. Briefly explain the importance of this, and the insight it gives us about P (x)

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