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# Prove that K^n satisfies axioms of vector spaces watch

1. Let K be a field and n greater than or equal to 0. Prove that K^n satisfies the following axioms of vector spaces:

1) (a + b) + c = a + (b + c)

2) There is a number 0 in S such that a + 0 = 0 + a = a for all a in S.

I don't understand what to do as I don't really understand what K^n is and how I'd go about proving these statements.

Thanks.
2. (Original post by Benniboi1)
Let K be a field and n greater than or equal to 0. Prove that K^n satisfies the following axioms of vector spaces:

1) (a + b) + c = a + (b + c)

2) There is a number 0 in S such that a + 0 = 0 + a = a for all a in S.

I don't understand what to do as I don't really understand what K^n is and how I'd go about proving these statements.

Thanks.
You can think of K^n as an n-tuple whose components are elements of K.

n=0 might be a problem though, unless it's just the zero element.

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Updated: January 23, 2014
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