<prompt> Tafuta matrix inayolingana na kuakisi juu ya vekta beginpmatrix 3 2 endpmatrix.  <response>: Acha mathbfv anzepmatrix x y endpmatrix, acha mathbfr iwe onyesho la mathbfv juu ya beginpmatrix 3 2 endpmatrix, na acha mathbfp iwe makadirio ya mathbfv kwenye beginpmatrix 3 2 endpmatrix.Kumbuka kuwa mathbfp ndio katikati ya mathbfv na mathbfr. Kwa hivyo, tunaweza kutumia mathbfp kukokotoa matrix ya kuakisi.asyukubwa wa kitengo 1 cm;jozi D, P, R, V;D 3,2;V 1.5,2;R tafakari0,0,DV;P V R2;chora-1,0--4,0;chora0,-1--0,3;chora0,0--D,Arrow6;chora0,0--V,nyekundu,Arrow6;chora0,0--R,bluu,Arrow6;chora0,0--P,kijani,Arrow6;choraV--R,iliyopigwa;lebomathbfp, P, S;lebomathbfv, V, N;lebomathbfr, R, SE;asyKutoka kwa fomula ya makadirio,anzaalignmathbfp jina la operetaproj_anzapmatrix 3 2 mwishopmatrix anzapmatrix x y mwishopmatrix fracanzapmatrix x y mwishopmatrix cdot anzapmatrix 3 2 mwishopmatrixanzapmatrix 3 2 mwishopmatrix cdoti anzapmatrix 3 2 mwishopmatrix anzapmatrix 3 2 mwishopmatrix frac3x 2y13 anzapmatrix 3 2 mwishopmatrix anzapmatrix frac9x 6y13 frac6x 4y13 endpmatrix.endalignKwa kuwa mathbfp ndio kitovu cha mathbfv na mathbfr,mathbfp fracmathbfv mathbfr2.Kishaanzaalignmathbfr 2 mathbfp - mathbfv 2 anzapmatrix frac9x 6y13 frac6x 4y13 endpmatrix - anzapmatrix x y mwishopmatrix anzapmatrix frac5x 12y13 frac12x - 5y13 endpmatrix anzapmatrix 513 1213 1213 -513 mwishopmatrix anzapmatrix x y mwishopmatrix.endalignKwa hivyo, matrix ni beginpmatrix 513 1213 1213 -513 endpmatrix. 