<prompt> Acha mathbfR iwe matrix ya kuakisi juu ya vekta beginpmatrix 3 1 endpmatrix. Find mathbfR2.  <response>: Acha mathbfv iwe vekta ya kiholela, na mathbfr iwe onyesho la mathbfv over beginpmatrix 3 1 endpmatrix, hivyo mathbfr mathbfR mathbfv.asyukubwa wa kitengo 1 cm;jozi D, P, R, V;D 3,1;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;choraV--R,iliyopigwa;lebomathbfv, V, NE;lebomathbfr, R, SE;asyKisha uakisi wa mathbfr ni mathbfv, so mathbfR mathbfr mathbfv. Hivyo,mathbfv mathbfR mathbfr mathbfR2 mathbfv.Kwa kuwa hii inashikilia kwa vekta zote mathbfv, mathbfR2 mathbfI anzapmatrix 1 0 0 1 mwishopmatrix. 