<prompt> MatrixmathbfA anzapmatrix 4 7 c d endpmatrixina sifa ambayo ukiambiwa thamani ya mathbfv, basi unaweza kupata thamani ya mathbfA mathbfv. Kokotoa c - d, ukichukulia kuwa c na d ni nambari halisi.  <response>: Acha mathbfv anzepmatrix x y mwishopmatrix. KishaanzaalignmathbfA mathbfv kushoto anzapmatrix 4 7 c d mwishopmatrix anzapmatrix x y mwishopmatrix kulia kushoto anzapmatrix 4x 7y cx dy mwishopmatrix kulia sqrt4x 7y2 cx dy2 sqrt16x2 56y 49y2 c2 x2 2cd xy d2 y2 sqrtc2 16 x2 2cd 56 xy d2 49 y2.endalignTunaambiwa kwamba tunaweza kupata thamani hii kutokana na thamani ya mathbfv sqrtx2 y2. Hii inashikilia ikiwa tu c2 16 d2 49 na 2cd 56 0. Hii inatupa c2 - d2 33 na cd -28. Squaring c2 - d2 33, tunapatac4 - 2c2 d2 d4 1089.Kishac4 2c2 d2 d4 1089 4c2 d2 1089 4 cdoti -282 4225.Hivyo, c2 d22 4225. Kwa kuwa c2 d2 lazima iwe isiyo hasi, c2 d2 sqrt4225 65.Kishac2 - 2cd d2 65 - 2-28 121,hivyo c - d 11.Kwa kazi nyingine, tunaweza kuonyesha kuwa c,d ni 7,-4 au -7,4. 