<prompt> Acha mathbfa anzepmatrix 7 -4 -4 mwishopmatrix na mathbfc anzapmatrix -2 -1 2 endpmatrix. Tafuta vekta mathbfb kiasi kwamba mathbfa, mathbfb, na mathbfc ni collinear, na mathbf b inagawanya pembe kati ya mathbfa na mathbfc.asyukubwa wa kitengo 0.5 cm;jozi A, B, C, O;A -2,5;B 1,3;O 0,0;C kiendeleziO, tafakariO,BA, A,B;choraO--A,Arrow6;choraO--B,Arrow6;choraO--C,Arrow6;kuchorainterpA,C,-0.1--interpA,C,1.1,iliyokatika;lebomathbfa, A, NE;lebomathbfb, B, NE;lebomathbfc, C, NE;asy  <response>: Laini kupitia mathbfa na mathbfc inaweza kuainishwa naanzapmatrix 7 - 9t -4 3t -4 6t mwishopmatrix.Kisha mathbfb ni ya fomu hii. Zaidi ya hayo, pembe kati ya mathbfa na mathbfb ni sawa na pembe kati ya mathbfb na mathbfc. Kwa hivyo,fracmathbfa cdot mathbfbmathbfa mathbfb fracmathbfb cdot mathbfcmathbfb mathbfc.Tunaweza kughairi vipengele vya mathbfb, ili kupatafracanzapmatrix 7 -4 -4 mwishopmatrix cdot anzapmatrix 7 - 9t -4 3t -4 6t mwishopmatrix kushoto anzapmatrix 7 -4 -4 mwishopmatrix kulia fracanzapmatrix 7 - 9t -4 3t -4 6t mwisho pmatrix cdot anzapmatrix -2 -1 2 mwishopmmatrixleft anzapmatrix -2 -1 2 mwishopmatrix kulia.Kishafrac77 - 9t -4-4 3t -4-4 6t9 frac7 - 9t- 2 -4 3t-1 -4 6t23Kutatua, tunapata t frac34. Kwa hivyo, mathbfb anzapmatrix 14 -74 12 mwishopmatrix. 