Let c1.....cnc1.....cn be scalars, not all zero, such that ∑ni=1ciai∑i=1nciai = 0 where aiai are column vectors in RnRn.
Consider the set of linear equations
where A=[a1.....an]A=[a1.....an] and b=∑ni=1aib=∑i=1nai. The set of equations has
(A) a unique solution at x=Jnx=Jn where JnJn denotes a nn-dimensional vector of all 1.
(B) no solution
(C) infinitely many solutions
(D) finitely many solutions