Let c₁ ..... c_n be scalars, not all zero, such that \[\sum\limits_{{\text{i}} = 1}^{\text{n}} {{{\text{c}}_{\text{i}}}{{\text{a}}_{\text{i}}}} = 0\]   where a_i are column vectors in Rⁿ. Consider the set of linear equations Ax = b where A = [a₁ ..... a_n] and \[{\text{b}} = \sum\limits_{{\text{i}} = 1}^{\text{n}} {{{\text{a}}_{\text{i}}}} .\]   The set of equations has

A. a unique solution at x = J_n where J_n denotes a n-dimensional vector of all 1

B. no solution

C. infinitely many solutions

D. finitely many solutions

Answer: Option C