Q^3/Non-trivial representation of 0/1/Exercise

Find, for the vectors

${\begin{pmatrix}7\\-5\\3\end{pmatrix}},\,{\begin{pmatrix}-4\\1\\-6\end{pmatrix}},\,{\begin{pmatrix}2\\8\\0\end{pmatrix}},\,{\begin{pmatrix}5\\-5\\8\end{pmatrix}}$

in ${}\mathbb {Q} ^{3}$, a non-trivial representation of the zero-vector.

Create a solution