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

Explain why \(\begin{pmatrix}1&2&3\\0&1&4\end{pmatrix}\) is not in reduced row echelon form.

Reduce \(\begin{pmatrix}1&2&5\\0&1&3\end{pmatrix}\) to reduced row echelon form.

Read the solution from the RREF augmented matrix \(\begin{pmatrix}1&0&4\\0&1&-7\end{pmatrix}\).

Reduce \(\begin{pmatrix}2&0&6\\0&3&12\end{pmatrix}\) to reduced row echelon form.

For RREF matrix \(\begin{pmatrix}1&0&2&5\\0&1&-1&3\end{pmatrix}\), write the solution set using free variable \(z=t\).

Determine whether \(\begin{pmatrix}1&0&0\\0&0&1\end{pmatrix}\) is the RREF of a consistent system in variables x and y.

Reduce \(\begin{pmatrix}1&1&4\\1&-1&0\end{pmatrix}\) to reduced row echelon form.

Identify pivot columns and free columns in \(\begin{pmatrix}1&0&3&0\\0&1&-2&0\end{pmatrix}\). Treat the last column as a constants column.

A learner says echelon form and reduced row echelon form are the same. Give a counterexample and explain.