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Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]] |
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Answer» SOLUTION :`[[1,OMEGA,omega^2],[omega,omega^2,1],[omega^2,1,omega]]=[[1+omega+omega^2,omega,omega^2],[omega+omega^2+1,omega^2,1],[omega^2+1+omega,1,omega]]` (REPLACING `C_1` by `C_1+C_2+C_3`) =`[[0,omega,omega^2],[0,omega^2,1],[0,1,omega]]=0(because 1+omega+omega^2)` |
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