- #1

RJLiberator

Gold Member

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## Homework Statement

Let

**v ∈**V and c

**∈ ℂ**, with c ≠ 0. Prove that if c

**v**=

**0**, then

**v**=

**0**.

## Homework Equations

Vector space axioms.

## The Attempt at a Solution

Simple proof overall, but I have one major clarification question.

**v**= 1

**v**

= (c^(-1)c)

**v**

= c^(-1) (c

**v**)

= c^(-1)

**0**

v=

v

**0**

My question is, in a complex vector space, is it safe to assume that c^(-1) exists in this proof?

If it does, I feel very confident about this proof.

If it doesn't then I need to do something else.

I don't see anywhere in the vector space axioms that states the multiplicative inverse exists.

But, it makes sense to me that an inverse does exist for any possible scalar choice here.