Oppgave: Finn redusert trappeform av [246114]\left[\begin{array}{cc|c}2&4&6\\1&1&4\end{array}\right][214164].
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12R1=[1 2∣3]\tfrac12 R_1=[1\ 2\mid 3]21R1=[1 2∣3]. R2−R1=[0 −1∣1]R_2-R_1=[0\ -1\mid 1]R2−R1=[0 −1∣1]. −R2=[0 1∣−1]-R_2=[0\ 1\mid -1]−R2=[0 1∣−1]. R1−2R2=[1 0∣5]R_1-2R_2=[1\ 0\mid 5]R1−2R2=[1 0∣5]. Resultat [10501−1]\left[\begin{array}{cc|c}1&0&5\\0&1&-1\end{array}\right][10015−1], altså x=5, y=−1x=5,\ y=-1x=5, y=−1. Kontroll: 2⋅5+4⋅(−1)=62\cdot5+4\cdot(-1)=62⋅5+4⋅(−1)=6 ✓.
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