Exercise 1.2.9

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Prove Corollaries 1 and 2 of Theorem $1.1$ and Theorem 1.2(c).

Jephian C.-H. Lin · Accepted Answer

For two zero vectors $0_0$ and $0_1$, by Thm 1.1 we have that $0_0+x=x=0_1+x$ implies $0_0=0_1$, where $x$ is an arbitrary vector. If for vector $x$ we have two inverse vectors $y_0$ and $y_1$. Then we have that $x+y_0=0=x+y_1$ implies $y_0=y_1$. Finally we have $$0a+1a=(0+1)a=1a=0+1a$$ and so $$0a=0.$$

Exercise 1.2.9

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Exercise 1.2.9

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