Math1231 Problems Using the Vector Axioms

Proof that 0u = 0

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