<prompt> Acha mathbfM iwe matrix kama hiyomathbfM anzapmatrix 2 -1 mwishopmatrix anzapmatrix 3 0 mwishopmatrix quad textna quad mathbfM anzapmatrix -3 5 mwishopmatrix anzapmatrix -1 -1 mwishopmatrix.Kokotoa mathbfM anzapmatrix 5 1 mwishopmatrix.  <response>: Tunaweza kujaribu kusuluhisha matrix mathbfM. Vinginevyo, tunaweza kujaribu kueleza beginpmatrix 5 1 endpmatrix kama mchanganyiko wa mstari wa beginpmatrix 2 -1 mwishopmatrix na anzapmatrix -3 5 mwishopmatrix. Hebuanzapmatrix 5 1 mwishopmatrix a anzapmatrix 2 -1 mwishopmatrix b anzapmatrix -3 5 mwishopmatrix anzapmatrix 2a - 3b -a 5b mwishopmatrix.Kwa hivyo, 5 2a - 3b na 1 -a 5b. Kutatua, tunapata a 4 na b 1, hivyoanzapmatrix 5 1 mwishopmatrix 4 anzapmatrix 2 -1 mwishopmatrix anzapmatrix -3 5 mwishopmatrix. Kwa hiyo,mathbfM anzapmatrix 5 1 mwishopmatrix 4 mathbfM anzapmatrix 2 -1 mwishopmatrix mathbfM startpmatrix -3 5 mwishopmatrix 4 anzapmatrix 3 0 mwishopmatrix anzapmatrix -1 -1 mwishopmatrix anza pmmatrix 11 -1 mwishopmatrix. 