Answer
$\mathrm{H}\mathrm{x}=0$ has solutions other than the trivial solution (by Th.8).
Work Step by Step
Using the IMT (Th.8),
$\mathrm{d}.\quad $ The equation $A\mathrm{x}=0$ has only the trivial solution.
and
$\mathrm{g}.\quad $ The equation $Ax=b$ has at least one solution for each $b$ in $\mathbb{R}^{n}$.
are both false when A=H and b=c.
Thus,
$\mathrm{H}\mathrm{x}=0$ has solutions other than the trivial solution (by Th.8).
