  We evaluate the determinant of a matrix whose entries are elliptic
hypergeometric terms and whose form is reminiscent of Sylvester matrices. A
hypergeometric determinant evaluation of a matrix of this type has appeared in
the context of approximation theory, in the work of Feng, Krattenthaler and Xu.
Our determinant evaluation is an elliptic extension of their evaluation, which
has two additional parameters (in addition to the base $q$ and nome $p$ found
in elliptic hypergeometric terms). We also extend the evaluation to a formula
transforming an elliptic determinant into a multiple of another elliptic
determinant. This transformation has two further parameters. The proofs of the
determinant evaluation and the transformation formula require an elliptic
determinant lemma due to Warnaar, and the application of two $C_n$ elliptic
formulas that extend Frenkel and Turaev's $_{10}V_9$ summation formula and
$_{12}V_{11}$ transformation formula, results due to Warnaar, Rosengren, Rains,
and Coskun and Gustafson.
