Solution
= Solution
<Algebraic stability> requires $b_i\geq0$ and positive semidefiniteness of
$$
\mathcal M=BA+A^TB-bb^T,\qquad B=\operatorname{diag}(b).
$$
The three weights are positive, but direct calculation gives
$$
\mathcal M_{11}=2b_1a_{11}-b_1^2=-\frac1{81}<0.
$$
A positive-semidefinite matrix cannot have a negative diagonal entry. Hence
$$
\boxed{\text{the method is not algebraically stable}.}
$$