  Working over an algebraically closed field $k$ of any characteristic, we
determine the matrix factorizations for the --- suitably graded --- triangle
singularities $f=x^a+y^b+z^c$ of domestic type, that is, we assume that
$(a,b,c)$ are integers at least two, satisfying $1/a+1/b+1/c>1$. Using work by
Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in
the Frobenius category of vector bundles on the weighted projective line of
weight type $(a,b,c)$. Equivalently, in a representation-theoretic context, we
can work in the mesh category of $\mathbb{Z}\tilde\Delta$ over $k$, where
$\tilde\Delta$ is the extended Dynkin diagram, corresponding to the Dynkin
diagram $\Delta=[a,b,c]$. Our work is related to, but in methods and results
different from, the determination of matrix factorizations for the
$\mathbb{Z}$-graded simple singularities by Kajiura-Saito-Takahashi. In
particular, we obtain symmetric matrix factorizations whose entries are scalar
multiples of monomials, with scalars taken from $\{0,\pm1\}$.
