<prompt> Kokotaanzapmatrix 3 -4 1 -1 mwishopmatrix2016.  <response>: Acha mathbfA anzepmatrix 3 -4 1 -1 endpmatrix. Kumbuka kwambaanzaalignmathbfA2 anzapmatrix 3 -4 1 -1 mwishopmatrix anzapmatrix 3 -4 1 -1 mwishopmatrix anzapmatrix 5 -8 2 -3 mwishopmatrix 2 anzapmatrix 3 -4 1 -1 mwishopmatrix - anzapmatrix 1 0 0 1 mwishopmatrix 2 mathbfA - mathbfI.endalignKwa hivyo, achamathbfB mathbfA - mathbfI anzapmatrix 3 -4 1 -1 mwishopmatrix - anzapmatrix 1 0 0 1 mwishopmatrix anzapmatrix 2 -4 1 -2 mwishopmatrix.Kisha mathbfB2 mathbf0, na mathbfA mathbfB mathbfI, hivyo kwa Nadharia ya Binomial,anzaalignmathbfA2016 mathbfB mathbfI2016 mathbfB2016 binom20161 mathbfB2015 binom20162 mathbfB2014 dots binom20162014 mathbfB2 binom20162015 mathbfB mathbfI 2016 mathbfB mathbfI 2016 anzapmatrix 2 -4 1 -2 mwishopmatrix anzapmatrix 1 0 0 1 mwishopmatrix anzapmatrix 4033 -8064 2016 -4031 mwishopmatrix.endalignKumbuka: Tunaweza kupanua mathbfB mathbfI2016 kwa kutumia Nadharia Binomial kwa sababu matrices mathbfB na mathbfI commute, yaani mathbfB mathbfI mathbfI mathbfB. Kwa ujumla, kupanua nguvu ya mathbfA mathbfB ni magumu. Kwa mfano,mathbfA mathbfB2 mathbfA2 mathbfA mathbfB mathbfB mathbfA mathbf B2,na bila kujua zaidi kuhusu mathbfA na mathbfB, hii haiwezi kurahisishwa. 