<prompt> Kwa nambari halisi a,b, na c, tumboanzapmatrix a b c b c a c a b mwishopmatrixhaibadiliki. Orodhesha thamani zote zinazowezekana zafracab c fracba c fracca b.  <response>: Kwa kuwa matrix haiwezi kubadilika, kiashiria chake ni 0, i.e.anzavmatrix a b c b c a c a b mwishovmatrix 0.Kiamuzi hupanuka kamaanzaalignanzavmatrix a b c b c a c a b mwishovmatrix a anzavmatrix c a a b mwishovmatrix - b anzavmatrix b a c b mwishovmatrix c anzavmatrix b c c a mwishovmatrix abc - a2 - bb2 - ac cab - c2 3abc - a3 - b3 - c3.endalignVigezo hivi kama3abc - a3 - b3 - c3 -a b ca2 b2 c2 - ab - ac - bc,hivyo ama a b c 0 au a2 b2 c2 - ab - ac - bc 0.Ikiwa a b c 0, basifracab c fracba c fracca b fraca-a fracb -b fracc-c -3.Sasa, tuseme a2 b2 c2 - ab - ac - bc 0. Kishaanzaaligna - b2 a - c2 b - c2 a2 - 2ab b2 a2 - 2ac c2 b2 - 2bc c2 2a2 b2 c2 - ab - ac - bc 0.endalignHii inalazimisha a b c, hivyofracab c fracba c fracca b frac32.Kwa hivyo, inawezekana maadili yafracab c fracba c fracca bni frac32 na iliyowekwa-3. 