Questions
If is cube root of unity and , then which of the following is correct
detailed solution
Correct option is D
The determinant of the coefficient matrix is Δ=1111ωω21ω2ω=1ω2-ω4-1ω-ω2+1ω2-ω=3ω2-ω ∵ω4=ω Also Δ1=a11bωω2cω2ω=aω2-ω4-bω-ω2+cω2-ω=a+b+cω2-ω Δ2=1a11bω21cω=1bω-cω2-1aω-c+1aω2-cb=a+bω2+cωω2-ω and Δ3=11a1ωb1ω2c=1cω-bω2-1c-aω2+1b-aω=a+bω+cω2ω2-ω ∴By Crammar's rule we have, x=Δ1Δ,y=Δ2Δand z=Δ3Δ. ⇒x=a+b+c3, y=a+bω2+cω3 and z=a+bω+cω23Similar Questions
If the system of equations , is consistent, then value of a is given by
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