Magic determinants of Somos sequences and theta functions

By means of an almost trivial statement of matrix algebra, we prove two conjectures proposed by Gosper and Schroeppel R.W. Gosper, R. Schroeppel, Somos sequence near-addition formulas and modular theta functions, arXiv:math.NT/0703470v1, 15 March 2007.] on near-addition formulas for 4- and 5-Somos sequences. A simplified proof for an elliptic analogue of this conjecture recently shown by Cooper and Toh in S. Cooper, P.C. Toh, Determinant identities for theta functions, J. Math. Anal. Appl. 347 (2008) 1-7] is also presented.