<prompt> Acha A -1,1,2, B 1,2,3, na C t,1,1, ambapo t ni nambari halisi. Tafuta eneo dogo zaidi linalowezekana la pembetatu ABC.  <response>: Acha mathbfa anzepmatrix -1 1 2 mwishopmatrix, mathbfb anzapmatrix 1 2 3 mwisho pmatrix, na mathbfc anzapmatrix t 1 1 endpmatrix. Kisha eneo la pembetatu ABC linatolewa naanzaalignfrac12 mathbfb - mathbfa nyakati mathbfc - mathbfa frac12 kushoto anzapmatrix 2 1 1 mwishopmatrix nyakati anzapmatrix t 1 0 -1 mwishopmatrix kulia frac12 kushoto anzapmatrix -1 3 t -1 - t mwishopmmatrix kulia frac12 sqrt-12 3 t2 -1 - t2 frac12 sqrt2t2 8t 11.endalignKukamilisha mraba kwa 2t2 8t 11, tunapata2t 22 3.Kwa hivyo, eneo dogo linalowezekana la pembetatu ni fracsqrt32. 