 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

If $\mathbf b$ is outside the <image of a linear map> $T_A$, there is no solution. Otherwise choose $\mathbf x_0$ with $A\mathbf x_0=\mathbf b$. By <2/a/ii>, a zero <kernel> gives a unique solution. If the <kernel> contains a nonzero <vector> $\mathbf z$, all
$$
\mathbf x_0+t\mathbf z,\qquad t\in\mathbb R,
$$
are solutions. They are distinct, since $(t-s)\mathbf z=0$ forces $t=s$. Hence there are infinitely many. These alternatives exhaust all possibilities.

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