Decide whether \(\begin{pmatrix}1&2&3\\0&4&5\\0&0&6\end{pmatrix}\) is in echelon form.

Decide whether \(\begin{pmatrix}0&1&2\\1&0&3\end{pmatrix}\) is in echelon form.

Identify the pivot columns in \(\begin{pmatrix}2&1&0&5\\0&3&-1&4\\0&0&0&1\end{pmatrix}\).

Use back substitution to solve the echelon system represented by \(\begin{pmatrix}1&2&1&6\\0&1&-1&1\\0&0&2&4\end{pmatrix}\).

Row reduce the first column of \(\begin{pmatrix}2&1&5\\4&3&11\end{pmatrix}\) to get an echelon form.

Solve the echelon system \(\begin{pmatrix}1&-1&0\\0&2&6\end{pmatrix}\) in variables x and y.

Explain why \(\begin{pmatrix}1&0&2\\0&0&0\\0&1&3\end{pmatrix}\) is not in echelon form.

For echelon matrix \(\begin{pmatrix}1&2&0&3\\0&0&1&4\end{pmatrix}\), identify pivot variables and free variables using variables x, y, z.

Determine whether the echelon matrix \(\begin{pmatrix}1&2&3\\0&0&1\end{pmatrix}\) represents an inconsistent system in variables x and y.

Find an echelon form of \(\begin{pmatrix}1&1&2\\2&3&5\\3&4&7\end{pmatrix}\).