Let V be a finite-dimensional vector space over a field F and f₁....f_nV* linear forms on V. Note the application

:Vfnv(f1(v),..fn(v)) a) Show that

Ker() = Ker(f₁)Ker(f₂) Ker(f_n)

b) Show that

Im() = Span(f₁, . .. , f_n)

c) Using the equalities shown in (a) and (b), show that a linear form f V* can be written as a linear combination f=a₁f₁+....+a_nf_n

if and only if Ker(f₁) ...Ker(f_n) Ker(f).