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For `alpha, beta, gamma in R`, let `A=[(alpha^(2),6,8),(3,beta^(2),9),(4,5,gamma^(2))]` and `B=[(2alpha,3,5),(2,2beta,6),(1,4,2gamma-3)]` |
Answer» We have, tr (A)=tr (B), `:. alpha^(2)+beta^(2)+gamma^(2)=2alpha+2beta+2 gamma-3` `implies (alpha^(2)-2alpha+1)+(beta^(2)-2beta+1)+(gamma^(2)-2gamma+1)=0` `implies (alpha-1)^(2)+(beta-1)^(2)+(gamma-1)^(2)=0` `implies alpha=1, beta=1, gamma=1` `:. (alpha^(-1)+beta^(-1)+gamma^(-1))=(1+1+1)=3` |
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