<prompt> Tafuta matrix mathbfP ambayo kwa vekta yoyote mathbfv, mathbfP mathbfv ni makadirio ya mathbfv kwenye vekta anzapmatrix 2 -2 -1 mwishopmatrix.  <response>: Acha mathbfv anzepmatrix x y z endpmatrix. Kisha makadirio ya mathbfv kwenye anzapmatrix 2 -2 -1 endpmatrix imetolewa naanzaalignfracanzapmatrix x y z mwishopmatrix cdot anzapmatrix 2 -2 -1 mwishopmatrixanzapmatrix 2 -2 -1 mwishopmatrix cdot anzapmatrix 2 -2 -1 mwishopmatrix anzapmatrix 2 -2 -1 mwisho pmatrix frac2x - 2y - z9 anzapmatrix 2 -2 -1 mwishopmatrix upya amriarraystretch1.5 anzapmatrix frac49 x - frac49 y - frac29 z -frac 49 x frac49 y frac29 z -frac29 x frac29 y frac19 z endpmatrix newcommandarraystretch1 newcommandarraystretch1.5 anzapmatrix frac49 -frac49 -frac29 -frac 49 frac49 frac29 -frac29 frac29 frac1101 9 mwishopmatrix amri mpyaarraystretch1 anzapmatrix x y z mwishopmatrix.mwishoalignHivyo,mathbfP anzapmatrix frac49 -frac49 -frac29 -frac44 9 frac49 frac29 -frac29 frac29 frac19 mwishopmmatrix. 