Lineares Gleichungssystem/Über Q sqrt(3)/Aufgabe

Löse das folgende lineare Gleichungssystem über dem Körper ${}K=\mathbb {Q} [{\sqrt {3}}]$ :

{}{\begin{pmatrix}2+{\sqrt {3}}&-{\sqrt {3}}\\{\frac {1}{2}}&-2-3{\sqrt {3}}\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}={\begin{pmatrix}1-{\sqrt {3}}\\4-2{\sqrt {3}}\end{pmatrix}}\,.

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