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
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`.
4 views
1 Answers
Correct Answer - 1
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`
4 views
Answered