Show that if ai are the components of a vector of coefficients satisfying aiaj i,j = 0,

Show that if ai are the components of a vector of coefficients satisfying aiajκ

i,j = 0, then aiκ

i,j = 0, aiκ

i,j,k = 0, aiκ

i,j,k,l = 0 and so on. Hence deduce that the choice of generalized inverse has no effect on the scalars derived in Section 2.8.