= Solution
{c}
\b[No.] A necessary condition for <consistency of a numerical method> is reproduction of the constant solution $y(x)=1$ of the <ordinary differential equation> $y'=0$. In a <linear multistep method> this gives
$$
\rho(1)=\sum_{j=0}^k\alpha_j=0.
$$
But the reverse <triangle inequality> gives, under the strict coefficient inequality,
$$
\boxed{|\rho(1)|\geq|\alpha_k|-\sum_{j=0}^{k-1}|\alpha_j|>0.}
$$
Thus the necessary <order conditions for a linear multistep method> already fail at order zero, regardless of the values of the $\beta_j$.
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