Prove that if m < n and if y_1, ... ,y_m are linear functionals on an n-dimensional vector space V, then there exists a nonzero vector x in V such that y_j(x)=0 for j=1,...,m. What does this result say about the solutions of linear equations?
For the second part: If we have m equations and n unknowns (with m<n), then a unique solution to the system doesn't exist.
For the first part, I started by letting
{x_1, ... , x_n} be a basis for V and
{y_1, ... , y_m} be a basis for V' (dual space)
Every x in V can be written as a linear combination of basis elements of V. I'm not sure where to go from here. Any help would be greatly appreciated!