<prompt> Kwa kuzingatia mathbfA anzapmatrix 0 1 -1 0 endpmatrix, kuna nambari chanya x na y kama hizox mathbfI y mathbfA2 mathbfA.Ingiza jozi iliyoagizwa x,y.  <response>: Tuna hiyoanzaalignx mathbfI y mathbfA kushoto x anzapmatrix 1 0 0 1 mwishopmatrix y anzapmatrix 0 1 -1 0 mwishopmmatrix kulia2 anzapmatrix x y -y x mwishopmatrix2 anzapmatrix x y -y x mwishopmatrix anzapmatrix x y -y x mwishopmatrix anzapmatrix x2 - y2 2xy -2xy x2 - y2 mwishopmatrix.endalignTunataka hii iwe sawa mathbfA beginpmatrix 0 1 -1 0 endpmatrix, kwa hivyo kwa kulinganisha coefficients, tunapata x2 - y2 0 na 2xy 1. Kisha x2 y2. Kwa kuwa x na y ni chanya, x y. Kisha 2x2 1, au x2 frac12, hivyo x,y left frac1sqrt2, frac1sqrt2 kulia. 