Let c1 … cn be scalars, not all zero, such that \(\mathop \sum \limits_{i = 1}^n {c_i}{a_i} = 0\) where ai are column vectors in Rn. Consider the set of linear equations
Ax = b
where A = \(\left[ {{a_1} \ldots {a_n}} \right]\;and\;b = \mathop \sum \limits_{i = 1}^n {a_i}\) The set of equations has1
a unique solution at x = Jn where Jn denotes a n-dimensional vector of all 1
2
no solution
3
infinitely many solutions
4
finitely many solutions