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For x, y in a vector space V, c in F, if cx=0 then c=0?

How do you prove this?

This is originally from Friedman, Linear Algebra, p.12.

To prove this, I can use a few facts:

(1) cancellation law

(2) 0, -x are unique

(3) 0x = 0

with basic vector space definition.

2. Relevant equations

3. The attempt at a solution

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# Homework Help: For x, y in a vector space V, c in F, if cx=0 then c=0?

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