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

Show that the axiom [itex]\vec{A} + (\vec{B} + \vec{C}) = (\vec{A} + \vec{B}) + \vec{C}[/itex] holds for polynomials of the form [itex]a_0 + a_1 x + a_2 x^2[/itex]

3. The attempt at a solution

I'm pretty new to writing proofs for linear algebra so my first question is should I be treating the polynomials as the vectors? That is, should I write something like,

[itex]a^A_0 + a^A_1 x + a^A_2 x^2 + (a^B_0 + a^B_1 x + a^B_2 x^2 + a^C_0 + a^C_1 x + a^C_2 x^2) = (a^A_0 + a^A_1 x + a^A_2 x^2 + a^B_0 + a^B_1 x + a^B_2 x^2) + a^C_0 + a^C_1 x + a^C_2 x^2[/itex]

?

I don't think this is correct since the polynomials aren't really vectors (right?). But I'm not sure how else to place these polynomials into the axioms.

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# Linear Algebra Axioms

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