Use Gauss-Jordan elimination to solve \(\begin{pmatrix}1&1&5\\1&-1&1\end{pmatrix}\).

Use Gauss-Jordan elimination to solve \(\begin{pmatrix}2&0&6\\0&5&10\end{pmatrix}\).

Use Gauss-Jordan elimination to solve \(\begin{pmatrix}1&2&7\\3&4&17\end{pmatrix}\).

Use Gauss-Jordan elimination to solve \(\begin{pmatrix}1&1&1&6\\0&1&-1&0\\0&0&1&2\end{pmatrix}\).

Use Gauss-Jordan elimination to determine whether \(\begin{pmatrix}1&2&3\\2&4&7\end{pmatrix}\) is consistent.

Use Gauss-Jordan elimination on \(\begin{pmatrix}1&2&0\\2&4&0\end{pmatrix}\) and describe the solutions.

Perform the first pivot step for \(\begin{pmatrix}0&1&2\\3&4&5\end{pmatrix}\) using Gauss-Jordan elimination.

Continue from \(\begin{pmatrix}1&2&5\\0&1&3\end{pmatrix}\) to RREF using Gauss-Jordan elimination.

Use Gauss-Jordan elimination to solve \(\begin{pmatrix}1&-1&2&3\\2&1&-1&0\\1&1&1&6\end{pmatrix}\).

A learner stops Gauss-Jordan elimination at \(\begin{pmatrix}1&2&5\\0&1&3\end{pmatrix}\) and reads \(x=5\), \(y=3\). Diagnose the error.