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Exercise 1.5.9

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It’s sufficient since if $u = tv$ for some $t \in 𝔽$ then we have $u - tv = 0$ . While it’s also necessary since if $au + bv = 0$ for some $a, b \in 𝔽$ with at least one of the two coefficients not zero then we may assume $a \neq 0$ and $u = - \frac{b}{a} v$ .

jephianlin

2011-06-27 00:00

Exercise 1.5.9

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