Vector space/Introductory example/Mulled wine/Example/Exercise

Does there exist a solution ${}(a,b,c)\in \mathbb {Q} ^{3}$ for the system of linear equations

${}a{\begin{pmatrix}1\\2\\11\\2\end{pmatrix}}+b{\begin{pmatrix}2\\2\\12\\3\end{pmatrix}}+c{\begin{pmatrix}3\\1\\20\\7\end{pmatrix}}={\begin{pmatrix}1\\2\\20\\5\end{pmatrix}}\,$

from

example?

Create a solution