Is it the Vilna Gaon who maintains that it is a mitzvah to eat matzah (to eat matzah, in addition to abstaining from chametz) every day and night during the week of Passover, or somebody else? The main opinion is that it is a mitzvah to eat it on the first night(s) and reshut (optional) during the rest of the holiday, but he differs. For some reason I remember it being him, but is it somebody else?
The Vilna Gaon's opinion followed those who explain that one is not obligated to eat matza on the latter 6.5 days of Pesach, but if one did so one has fulfilled a Biblical injunction. This is parallel to the rule by Sukkot whereby one must eat in the Sukkah on the first night, but for the remaining 6.5 days one may survive on fruits and drinks and never sit in the Sukkah (except, of course, sleeping because one cannot go 72 hours without sleeping, cf. Shevuot 25a); yet we know that if one does sit in the Sukkah he has fulfilled a Biblical injunction.
The only reason that the obligation to eat Matza on the latter 6.5 days is called a "Reshut -- optional" is to contrast it with the obligation of the first night which is a "Chovah -- mandatory".