Let \(c_{1},\ldots,c_{n}\) be scalars, not all zero, such that…

Let $c_{1},\ldots,c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}=0$, where $a_{i}$ are column vectors in $\mathbb{R}^{n}$.

Consider the set of linear equations

$Ax = b$

where $A=\left [ a_{1}.....a_{n} \right ]$ and $b=\sum_{i=1}^{n}a_{i}$. The set of equations has