 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

\b[No.] Here $A$ has more rows than columns, which does not force a nonzero <kernel>. For example, with $m=1$, $n=2$,
$$
A=\begin{pmatrix}1\\0\end{pmatrix},\qquad
\mathbf b=\begin{pmatrix}0\\0\end{pmatrix},
$$
the <linear system> has the unique solution $x=0$. With the same $A$ and $\mathbf b=(0,1)^T$ it has no solution at all.

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