- #1
Mr Davis 97
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Homework Statement
Let ## \mathbb{V} = \{0 \}## consist of a single vector ##0## and define ##0 + 0 = 0## and ##c0 = 0## for each scalar in ##\mathbb{F}##. Prove that ##\mathbb{V}## is a vector space.
Homework Equations
The Attempt at a Solution
Proving that the first six axioms of a vector space are true is trivial, I am just on the distributive axioms.
So if I want to show that ##a(x + y) = ax + ay## is true, where a is a scalar and x and y are vectors, is it sufficient to make the argument that ##a(0 + 0) = a0 = 0 = a0 + a0##? Does this show that a distributes over the vector ##0##?