A Theorem of Linear Functions

In this note,the following theorem is proved:let f, f₁, f₂, …, f_m be linear functions on the vector space V, f is a linear combination of f₁, f₂, …, f_m if and only if ???19960218??? ker (f₁) ker(f).where ker (g) is the kernel of linear function g(i.e. ker (g)=α|α∈V&g(α)=0).