Linear system/n variables/Solution space is (a 1,...,a n)/Exercise

Let ${}K$ be a field, and let

${}{\begin{pmatrix}a_{1}\\\vdots \\a_{n}\end{pmatrix}}\in K^{n}\,$

be a nonzero vector. Find a linear system of equations in ${}n$ variables with ${}n-1$ equations, whose solution space is exactly

${\left\{\lambda {\begin{pmatrix}a_{1}\\\vdots \\a_{n}\end{pmatrix}}\mid \lambda \in K\right\}}.$

Create a solution