<prompt> Kwa baadhi ya matrix mathbfP anzapmatrix a b c d endpmatrix yenye maingizo kamili yasiyo na nambari,anzapmatrix 4 3 -1 0 mwishopmatrix mathbfP-1 anzapmatrix 1 0 0 3 mwishopmatrix mathbfP.Tafuta thamani ndogo kabisa ya a b c d.  <response>: Kutoka kwa mlinganyo anzapmatrix 4 3 -1 0 endpmatrix mathbfP-1 anzapmatrix 1 0 0 3 mwisho pmatrix mathbfP, tunaweza kuzidisha pande zote mbili kwa mathbfP upande wa kushoto, kupatamathbfP anzapmatrix 4 3 -1 0 mwishopmatrix anzapmatrix 1 0 0 3 endpmatrix mathbfP .Kishaanzapmatrix a b c d mwishopmatrix anzapmatrix 4 3 -1 0 mwishopmatrix anzapmatrix 1 0 0 3 mwishopmatrix anzapmatrix a b c d mwishopmatrix,hivyoanzapmatrix 4a - b 3a 4c - d 3c mwishopmatrix anzapmatrix a b 3c 3d mwishopmatrix.Tukilinganisha maingizo, sisi pata 4a - b a,3a b, 4c - d 3c, na 3c 3d. Hizi hupunguza hadi b 3a na c d, hivyoa b c d a 3a c d 4a 2d.Kwa kuwa a, b, c, na d zote ni nambari kamili zisizo na maana, tunapunguza hii kwa kuchukua a pm 1 na d pm 1, katika hali ambayo 4a 2d 6. 