What does \(RREF\) stand for?

In RREF, what value must every leading entry in a nonzero row have?

In RREF, what must be true about the other entries in a pivot column?

Where must \(zero\) rows appear in RREF?

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

For variables \((x,y,z)\), the RREF has pivot columns \(1\) and \(3\). Which variable is free?

Read the equations from \(\left(\begin{array}{ccc|c}1&0&2&7\\0&1&-1&3\end{array}\right)\).

Is \(\begin{pmatrix}1&2&0\\0&1&0\end{pmatrix}\) in RREF? Explain.

Find the solution set from \(\left(\begin{array}{ccc|c}1&0&2&5\\0&1&-3&4\end{array}\right)\).

Decide whether \(\begin{pmatrix}1&0&0\\0&0&1\\0&0&0\end{pmatrix}\) is in RREF.

Explain why a \(non\)-pivot variable in RREF is called free.

Why is \(RREF\) useful for checking whether a system has infinitely many solutions?

Find the solution set from \(\left(\begin{array}{cccc|c}1&0&2&0&3\\0&1&-1&0&5\\0&0&0&1&-2\end{array}\right)\) for variables \((w,x,y,z)\).

A matrix in RREF has \(5\) variable columns and pivot columns \(1\), \(3\), and \(5\), with no inconsistent row. How many parameters are needed in the solution set?

For what values of \(a\) is \(\begin{pmatrix}1&a\\0&1\end{pmatrix}\) in RREF?

For which values of \(a\) is \(\begin{pmatrix}1&0&a\\0&1&2\\0&0&0\end{pmatrix}\) in RREF?

An augmented RREF for variables \((x,y,z)\) is \(\left(\begin{array}{ccc|c}1&0&a&2\\0&1&1&3\\0&0&0&0\end{array}\right)\). Describe the solution set in terms of \(a\).

Diagnose the error: from \(\left(\begin{array}{ccc|c}1&0&2&4\\0&1&-1&5\end{array}\right)\), a learner says \(z=0\) because there is no pivot in the \(z\)-column.

Explain why RREF is unique even though different valid row-operation paths may be used to reach it.

A learner checks RREF by looking only for leading \(1\)s. Give a counterexample and explain the missing conditions.