Below is a proof of Theorem 4.1.1 (b): For the zero vector ?0 inany vector space V and k ? R, k?0 = ?0.
Justify for each of the eight steps why it is true.
k?0+k?0=k(?0+?0)
= k ?0
k?0 is in V
and therefore ?(k?0) is in V .
It follows that (k?0 + k?0) + (?k?0) = (k?0) + (?k?0)
and thus k?0 + (k?0 + (?k?0)) = (k?0) + (?k?0).
We conclude that k?0 + ?0 = ?0
and so k?0 = ?0, as desired.
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