<prompt> Tafuta matrix inayolingana na kuakisi juu ya vekta beginpmatrix -1 3 endpmatrix.  <response>: Acha mathbfv anzepmatrix x y endpmatrix, acha mathbfr iwe onyesho la mathbfv juu ya beginpmatrix -1 3 endpmatrix, na acha mathbfp iwe makadirio ya mathbfv kwenye beginpmatrix -1 3 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 -1,3;V 0.5,2.5;R tafakari0,0,DV;P V R2;chora-3,0--2,0;chora0,-1--0,4;chora0,0--D,Arrow6;chora0,0--V,nyekundu,Arrow6;chora0,0--R,bluu,Arrow6;chora0,0--P,kijani,Arrow6;choraV--R,iliyopigwa;lebomathbfp, P, SW;lebomathbfv, V, E;lebomathbfr, R, SW;asyKutoka kwa fomula ya makadirio,anzaalignmathbfp jina la operetaproj_anzapmatrix -1 3 mwishopmatrix anzapmatrix x y mwishopmatrix fracanzapmatrix x y mwishopmatrix cdot anzapmatrix -1 3 mwishopmatrixanzapmatrix -1 3 mwisho pmatrix cdot anzapmatrix -1 3 mwishopmatrix anzapmatrix 2 -3 mwishopmatrix frac-x 3y10 anzapmatrix -1 3 mwishopmatrix anzapmatrix fracx - 3y10 frac-3x 9y10 endpmatrix.endalignKwa kuwa mathbfp ndio kitovu cha mathbfv na mathbfr,mathbfp fracmathbfv mathbfr2.Kishaanzaalignmathbfr 2 mathbfp - mathbfv 2 anzapmatrix fracx - 3y10 frac-3x 9y10 mwishopmatrix - anzapmatrix x y mwishopmatrix anzapmatrix frac-4x - 3y5 frac-3x 4y5 endpmatrix anzapmatrix -45 -35 -35 45 mwishopmatrix anzapmatrix x y mwishopmatrix.endalignKwa hivyo, matrix ni beginpmatrix -45 -35 -35 45 endpmatrix. 