answer only b please will full explanations please Prove eac

answer only b please will full explanations please

Prove each of the following for vectors u and v and scalars a and b. If av = 0, then a = 0 or v = 0. If av = bv and v 0, then a = b.

Solution

b) Given that av = bv

                   add -bv on bothsides,

                      av + (-bv) = bv + (-bv)

                       av + (-b) v = 0

                       (a-b) v = 0

                       a-b = 0    [ since v not equal to 0 ]

                       a = b

       Therefore,

              a = b