Question

Assume ( V ) is finite-dimensional with basis ( v₁, ldots, vₙ ). Prove that if ( S = v₁, ldots, vₖ ), then ( ann(S) ) is the subspace spanned by ( vₖ₊₁, ldots, vₙ ).

a) ( ann(S) = span(vₖ₊₁, ldots, vₙ) )
b) ( ann(S) = span(vₖ₋₁, ldots, vₙ) )
c) ( ann(S) = span(v₁, ldots, vₖ) )
d) ( ann(S) = span(v₁, ldots, vₖ₋₁) )