Math1231 Problems Using the Vector Axioms

## Proof that 0u = 0

- Add u to LHS to create 0u + u
- Use axiom 9 to create this as u(0 + 1)
- Add 0+1 (this is just done normally) to get 1(u)
- Use axiom 8 to rewrite this as u
- Therefore 0u + u = u
- Take u away from both sides to get 0u + u – u = u – u
- Use axiom 9 to rewrite this as 0u + u(1-1) = 0
- Subtract 1 from 1 (done normally) to get 0u + 0u = 0
- Use axiom 9 again to get u(0 + 0) = 0
- Add 0+0 to get u(0) = 0
- Use axiom 7 (associative law of scalar multiplication) to get 0u = 0

page revision: 3, last edited: 22 Jul 2011 01:15