<prompt> HebumathbfA anzapmatrix 4 1 -9 -2 mwishopmatrix.Kokotoa mathbfA100.  <response>: Kumbuka hiloanzaalignmathbfA2 anzapmatrix 4 1 -9 -2 mwishopmatrix anzapmatrix 4 1 -9 -2 mwishopmatrix anzapmatrix 7 2 -18 -5 mwishopmatrix 2 anzapmatrix 4 1 -9 -2 mwishopmatrix - anzapmatrix 1 0 0 1 mwishopmatrix 2 mathbfA - mathbfI.mwishoalignKisha mathbfA2 - 2 mathbfA mathbfI 0, hivyomathbfA - mathbfI2 mathbfA2 - 2 mathbfA mathbfI mathbf0.Hivyo, turuhusumathbfB mathbfA - mathbfI anzapmatrix 4 1 -9 -2 mwishopmatrix - anzapmatrix 1 0 0 1 mwishopmatrix anzapmatrix 3 1 -9 -3 mwishopmatrix.Kisha mathbfB2 mathbf0, na mathbfA mathbfB mathbfI, hivyo kwa Nadharia ya Binomial,anzaalignmathbfA100 mathbfB mathbfI100 mathbfB100 binom1001 mathbfB99 binom1002 mathbfB98 dots binom10098 mathbfB2 binom10099 mathbfB mathbfI 100 mathbfB mathbfI 100 anzapmatrix 3 1 -9 -3 mwishopmatrix anzapmatrix 1 0 0 1 mwishopmatrix anzapmatrix 301 100 -900 -299 mwishopmatrix.endalignKumbuka: Tunaweza kupanua mathbfB mathbfI100 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. 