Describe the solution set of x + \(y=3\) in \(\mathbb R^2\) using parameter \(t=y\).

Describe the solution set represented by RREF \(\begin{pmatrix}1&0&2&4\\0&1&-1&5\end{pmatrix}\) using \(z=t\).

Classify the system represented by \(\begin{pmatrix}1&0&2\\0&1&-3\end{pmatrix}\) as having no solution, one solution, or infinitely many solutions.

Classify the system represented by \(\begin{pmatrix}1&2&0\\0&0&1\end{pmatrix}\) in variables x and y.

Classify the system represented by \(\begin{pmatrix}1&2&0\\0&0&0\end{pmatrix}\) in variables x and y.

Write the solution set of x - 2y + \(z=0\) in \(\mathbb R^3\) using \(y=s\) and \(z=t\).

Find the solution set of the homogeneous system represented by \(\begin{pmatrix}1&0&-3&0\\0&1&2&0\end{pmatrix}\), using \(z=t\).

Explain why a homogeneous linear system always has at least one solution.

For the solution set \((x, y, z)\) = \((1, 2, 0)\) + t(3, -1, 4), find the point corresponding to \(t=-2\).

A learner says a system with a free variable has no solution because one variable is unknown. Diagnose the error.