質問: if `|(a^(2)+lamda^(2),ab+clamda,ca-blamda),(ab-clamda,b^(2)+lamda^(2),bc+alamda),(ca+blamda,-bc+alamda, c^(2)+lamda^(2))||(lamda,c,-b),(-c,lamda,a),(b,-a,lamda)|=(1+a^(2)+b^(2)+c^(2))^(3)`, then find the value of `lamda`. if `|(a^(2)+lamda^(2),ab+clamda,ca-blamda),(ab-clamda,b^(2)+lamda^(2),bc+alamda),(ca+blamda,-bc+alamda, c^(2)+lamda^(2))||(lamda,c,-b),(-c,lamda,a),(b,-a,lamda)|=(1+a^(2)+b^(2)+c^(2))^(3)`, then find the value of `lamda`.
回答: answer: 1 solution: we observe that the elements in the prefactor are the cofactors of the corresponding elements of the post factor. hence l.h.s. `=|(lamda, c, -b),(-c, lamda, a),(b, -a, lamda)|^(3)=[lamda(lamda^(2)+a^(2)+b^(2)+c^(2))]^(3)=(1+a^(2)+b^(2)+c^(2))^(2)implieslamda=1`