Solution
= Solution
{c}
\b[No.] The <rank-nullity theorem> gives
$$
\dim\ker T_A=m-\operatorname{rank}T_A\geq m-n>0,
$$
but this guarantees infinitely many solutions only when the <linear system> is consistent. For a counterexample take
$$
n=1,\quad m=2,\quad A=\begin{pmatrix}0&0\end{pmatrix},\quad\mathbf b=(1).
$$
There is no solution, since the left side always vanishes.