<prompt> Tafuta matrix ambayo inalingana na kuonyesha kwenye vekta beginpmatrix 2 -3 endpmatrix.  <response>: Kutoka kwa fomula ya makadirio, makadirio ya beginpmatrix x y endpmatrix kwenye beginpmatrix 2 -3 endpmatrix nianzaalignjina la operetaproj_anzapmatrix 2 -3 mwishopmatrix anzapmatrix x y mwishopmatrix fracanzapmatrix x y mwishopmatrix cdot anzapmatrix 2 -3 mwishopmatrixanzapmatrix 2 -3 mwishopmatrix cdot anzapmatrix 2 -3 mwishopmatrix anzapmatrix 2 -3 mwishopmatrix frac2x - 3y13 anzapmatrix 2 -3 mwishopmatrix anzapmatrix frac4x - 6y13 frac-6x 9y13 endpmatrix.endalignIli kupata matrix ya makadirio, tunaandika vekta hii kama bidhaa ya matrix na vekta beginpmatrix x y endpmatrix:anzapmatrix frac4x - 6y13 frac-6x 9y13 endpmatrix beginpmatrix 413 -613 -613 913 mwishopmatrix anzapmatrix x y mwishopmatrix.Kwa hivyo, matrix ya mageuzi haya ni beginpmatrix 413 - 613 -613 913 mwishopmatrix. 