  This paper is primarily concerned with the first cohomology of
$\frak{gl}_{0|2}$ with coefficients in the generalized Witt Lie superalgebra,
where $\frak{gl}_{0|2}$ is a subalgebra of the general linear Lie superalgebra.
The derivations and inner derivations from $\frak{gl}_{0|2}$ into submodules of
the generalized Witt Lie superalgebra are represented by matrices,
respectively. Then the first cohomology of $\frak{gl}_{0|2}$ with coefficients
in the generalized Witt Lie superalgebra is completely determined by matrices.
