# Prove that u + v = v + u for any u and v in R^n.

First note that for a, b \in R , a+b = b+ a . This is the commutative property of addition (scalar).

Suppose u, v \in R^n are n-dimensional vectors such that:

u = <u_1, u_2, ..., u_n> and

v = <v_1, v_2, ..., v_n> .

u + v =...

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First note that for a, b \in R , a+b = b+ a . This is the commutative property of addition (scalar).

Suppose u, v \in R^n are n-dimensional vectors such that:

u = <u_1, u_2, ..., u_n> and

v = <v_1, v_2, ..., v_n> .

u + v = <u_1 + v_1, u_2 + v_2, ..., u_n + v_n>

By the commutative property of addition,

u + v = <u_1 + v_1, u_2 + v_2, ..., u_n + v_n> 

= <v_1 + u_1, v_2 + u_2, ..., v_n + u_n> = v + u.`

Therefore, for any n-dimensional vectors u and v, u + v = v + n.

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