= Solution
For <algebraic stability of a Runge-Kutta method>, the weights must be nonnegative and
$$
M=BA+A^TB-bb^T,\qquad B=\operatorname{diag}(b),
$$
must be a <positive semidefinite matrix>. Here all weights are positive, but direct calculation gives
$$
M=\frac1{36}\begin{pmatrix}-1&1&0\\1&0&-1\\0&-1&1\end{pmatrix}.
$$
In particular $e_1^TMe_1=-1/36<0$; equivalently, its <eigenvalues> are $0,\pm\sqrt3/36$. Therefore \b[the method is not <algebraically stable>]. This does not contradict its <A-stability>: <algebraic stability> is a stronger condition designed to guarantee nonlinear <B-stability> through the <Runge-Kutta contractivity identity>.
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