<prompt> Ikiwa mathbfa anzapmatrix 1 1 1 endpmatrix, basi pata vekta mathbfv kiasi kwamba mathbfa cdot mathbf v 2 na mathbfa nyakati mathbfv anzapmatrix 1 -2 1 mwishopmatrix.  <response>: Acha mathbfv anzepmatrix x y z endpmatrix. Kisha kutoka kwa mlinganyo mathbfa cdot mathbfv 2, x y z 2.Pia,mathbfa nyakati mathbfv anzapmatrix 1 1 1 mwishopmatrix nyakati anzapmatrix x y z mwishopmatrix anzapmatrix -y z x - z -x y mwishopmatrix.Kwa hiyo,anzaalign-y z 1, x - z -2, -x y 1.endalignKutatua mfumo huu, pamoja na equation x y z 2, tunapata x -frac13, y frac23 , na z frac53. Hivyo, mathbfv beginpmatrix -13 23 53 endpmatrix . 