<prompt> Acha mathbfA iwe matrix kama hiyomathbfA anzapmatrix 3 1 0 mwishopmatrix anzapmatrix 2 4 -3 mwishopmatrix quad maandishina quad mathbfA anzapmatrix -5 2 2 mwishopmatrix anzapmatrix 0 -5 -5 mwishopmatrix.Tafuta mathbfA anzapmatrix -13 3 4 mwishopmatrix.  <response>: Ili kupata mathbfA beginpmatrix -13 3 4 endpmatrix, ninahitaji kuelezea vekta beginpmatrix -13 3 4 mwisho pmatrix kama mseto wa mstari wa vekta beginpmatrix 3 1 0 endpmatrix na beginpmatrix -5 2 2 endpmatrix , ambayo hutolewa na kuzidisha matrix. Ninaweza kuandika beginpmatrix -13 3 4 mwishopmatrix x anzapmatrix 3 1 0 mwishopmatrix y anzapmatrix -5 2 2 endpmatrix, ambapo x na y ni mikwaruzo isiyojulikana. Hii inanipa mfumo wa hesabu tatu katika anuwai mbili:anzailiyopangwa-13 3x - 5y 3 x 2y 4 2yendaligned Ninaweza kutatua kwa y kutoka mlinganyo wa tatu: y 2. Kisha ninaweza kuunganisha y 2 kwenye mlinganyo wa pili na kutatua x: x 3 - 4 -1. Sasa kwa kuwa nina x -1 na y 2, ninaweza kutumia mali ya kusambaza ya kuzidisha matrix na hesabu zilizopewa kupata mathbfA beginpmatrix -13 3 4 mwishopmatrix:anzailiyopangwamathbfA anzapmatrix -13 3 4 mwishopmatrix mathbfA x anzapmatrix 3 1 0 mwishopmatrix y anzapmatrix -5 2 2 mwishopmmatrix mathbfA -1 anzapmatrix 3 1 0 mwishopmatrix 2 anzapmatrix -5 2 2 mwishopmatrix -1 mathbfA anzapmatrix 3 1 0 mwishopmatrix 2 mathbfA anzapmatrix -5 2 2 mwishopmatrix -1 anzapmatrix 2 4 -3 mwishopmatrix 2 anzapmatrix 0 -5 -5 mwishopmatrix anzapmatrix -2 -4 3 mwishopmatrix anzapmatrix 0 -10 -10 mwishopmatrix anzapmatrix -2 -14 -7 mwishopmatrixmwishoimepangiliwa 