= Solution
For <algebraic stability>, the weights must be nonnegative and the real <symmetric matrix> $M=BA+A^TB-bb^T$, where $B=\operatorname{diag}(b)$, must be a <positive semidefinite matrix>.
The weights are positive, but $a_{11}=0$ and $b_1=1/6$, so
$$
M_{11}=2b_1a_{11}-b_1^2=-\frac1{36}<0.
$$
A <positive semidefinite matrix> cannot have a negative diagonal entry, as its <quadratic form> at the first <standard basis> vector would be negative. Thus this <Lobatto IIIA method> is \b[not <algebraically stable>], despite its <A-stability>.
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