<prompt> Makadirio huchukua beginpmatrix 1 -2 endpmatrix hadi beginpmatrix frac32 -frac32 endpmatrix . Je, makadirio huchukua vekta gani beginpmatrix -4 1 endpmatrix?  <response>: Kwa kuwa makadirio ya beginpmatrix 1 -2 endpmatrix ni beginpmatrix frac32 -frac32 end pmatrix, vekta inayokadiriwa ni kizidishi cha scalar cha beginpmatrix frac32 -frac32 endpmatrix. Hivyo, tunaweza chukulia kuwa vekta inayokadiriwa ni beginpmatrix 1 -1 endpmatrix.asyusepackageamsmath;ukubwa wa kitengo 1 cm;jozi A, B, O, P, Q;O 0,0;A 1,-2;P 32,-32;B -4,1;Q -52,52;chora-4,0--2,0;chora0,-2--0,3;choraO--A,Arrow6;choraO--P,Arrow6;kuchoraA--P,dashed,Arrow6;choraO--B,Arrow6;choraO--Q,Arrow6;kuchoraB--Q,dashed,Arrow6;leboanzapmatrix 1 -2 mwishopmatrix, A, S;lebobeginpmatrix frac32 -frac32 endpmatrix, P, SE;leboanzapmatrix -4 1 mwishopmatrix, B, W;asyKwa hivyo, makadirio ya beginpmatrix -4 1 endpmatrix nijina la operetaproj_anzapmatrix 1 -1 mwishopmatrix anzapmatrix -4 1 mwishopmatrix fracanzapmatrix - 4 1 mwishopmatrix cdot anzapmatrix 1 -1 mwishopmatrixanzapmatrix 1 -1 mwishopmatrix cdot anzapmatrix 1 -1 mwishopmatrix anzapmatrix 1 -1 mwishopmatrix frac-52 anzapmatrix 1 -1 mwishopmatrix anzapmatrix -52 52 mwishopmatrix. 