Write the augmented matrix for the system x + 2y = 5 and 3x - \(y=4\).

Write the augmented matrix for 2x - y + \(z=1\), x + 3y = 7, and -x + \(z=0\), using variable order x, y, z.

Convert the augmented matrix \(\begin{pmatrix}1&-2&3\\0&4&-8\end{pmatrix}\) into a system using variables x and y.

Convert \(\begin{pmatrix}2&0&-1&5\\1&3&4&-2\end{pmatrix}\) into equations using variables x, y, z.

For the augmented matrix \(\begin{pmatrix}1&2&0\\0&0&3\end{pmatrix}\), explain why the represented system is inconsistent.

For \(\begin{pmatrix}1&0&4\\0&1&-2\end{pmatrix}\), read off the solution to the system in variables x and y.

Write the coefficient matrix and constants vector for x - y + 2z = 6 and 3x + \(z=-1\).

A system has coefficient matrix \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\) and constants vector \(\begin{pmatrix}5\\6\end{pmatrix}\). Write its augmented matrix.

Using variables x, y, z, identify the missing entry a in \(\begin{pmatrix}1&a&2&4\end{pmatrix}\) if the row represents x - 3y + 2z = 4.

A learner writes the augmented matrix for x + \(y=2\) and x - \(y=0\) as \(\begin{pmatrix}1&1\\1&-1\\2&0\end{pmatrix}\). Diagnose the error.