(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(i) Set of all row vectors:(a1,....,an), aj in K; addition, multiplication defined componentwise. This space is denoted as Kn.

(ii) Set of all real valued functions f(x) defined on the real line, K = R.

(iii) Set of all functions with values in K, defined on an arbitrary set S.

(iv) Set of all polynomials of degree less than n with coefficients in K.

2. Relevant equations

1) Show that (i) and (iv) are isomorphic

2) Show that if S has n elements, (i) is the same as (iii)

3) Show that when K = R, (iv) is isomorphic with (iii) when S consists of n distinct points of R.

3. The attempt at a solution

I've solved 1), but I cannot solve others. I think that problem is that I don't understand definition of (iii).

Could someone please help me?

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# Homework Help: How to find Insomorphism

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