1.

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

Answer»


Solution :We observe that the elements in the prefactor are the confactors of the correspoinding 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))^(3)implieslamda=1`


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