<prompt> Acha mathbfa, mathbfb, mathbfc iwe vekta tatu ilimathbfa nyakati mathbfb anzapmatrix 6 -7 3 mwishopmatrix, quad mathbfa nyakati mathbfc startpmatrix 4 7 2 mwishopmatrix, quad mathbfb mara mathbfc anzapmatrix 1 -7 18 mwishopmatrix .Kokotoa 2 mathbfb - mathbfa mara 3 mathbfc mathbfa.  <response>: Ili kurahisisha shida hii, nitatumia sifa zifuatazo za bidhaa ya msalaba: ni ya pande mbili, ikimaanisha kwamba inasambaza juu ya kuongeza na kuzidisha kwa scalar, na ni anticommutative, ikimaanisha kuwa mathbfu times mathbfv - mathbfv mara mathbfu kwa vekta zozote mathbfu na mathbfv. Kwa kutumia sifa hizi, ninaweza kuandika upya usemi uliotolewa kamaanzaalign2 mathbfb - mathbfa nyakati 3 mathbfc mathbfa 6 mathbfb nyakati mathbfc 2 mathbf b nyakati mathbfa - 3 mathbfa nyakati mathbfc - mathbfa nyakati mathbfa 6 mathbfb nyakati mathbfc - 2 mathbfa nyakati mathbfb - 3 mathbfa nyakati mathbfc - 0 6 anzapmatrix 1 -7 18 mwishopmatrix - 2 anzapmatrix 6 -7 3 mwishopmatrix - 3 anzapmatrix 4 7 2 mwishopmmatrix anzapmatrix 6 - 12 - 12 -42 14 - 21 108 - 6 - 6 mwishopmatrix anzapmatrix -18 -49 96 mwishopmatrix.endalign Kwa hivyo, jibu la mwisho ni 