Solution
= Solution
{c}
By <2/c/i>, a free choice of $x_3$ is possible precisely when $\lambda=5$ and $\mu=2$. Thus
$$
\boxed{\text{infinitely many solutions}\iff(\lambda,\mu)=(5,2).}
$$
The complete <solution set of a linear system> is
$$
\boxed{\mathbf x=\begin{pmatrix}1\\2\\0\end{pmatrix}
+t\begin{pmatrix}-2\\-5\\1\end{pmatrix},\quad t\in\mathbb R.}
$$
The direction <vector> spans the <kernel>, and the displayed <straight line> is the entire <solution set of a linear system>.