Theorem 10 (Exercise):

10

We have 0_V = w_1 + v = w_2 + v. Subtracting v we have:

(w_1 + v) - v = (w_2 + v) - v

then using associativity:

w_1 + (v - v) = w_2 + (v - v)

noting that w_1 + (v - v) = w_1 + 0_V = w_1 and w_2 + (v - v) = w_2 + 0_V = w_2 we have w_1 = w_2.

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