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If omega!=1 is a cube root of unity and ...

If `omega!=1` is a cube root of unity and `x+y+z!=0,` then prove that `|[x/(1+omega), y/(omega+omega^2),z/(omega^2+1)],[y/(omega+omega^2),z/(omega^2+1),x/(1+omega)],[(z)/(omega^2+1),x/(1+omega),y/(omega+omega^2)]|=0` if `x=y=z`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. Show that |^x Cr^x C(r+1)^x C(r+2)^y Cr^y C(r+1)^y C(r+2)^z Cr^z C(r+1...

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  3. If omega!=1 is a cube root of unity and x+y+z!=0, then prove that |[x/...

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  4. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  6. If alpha,beta,gamma are the angles of a triangle and system of equatio...

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  7. Without expanding the determinants, prove that |(103, 115, 114), (111,...

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  8. Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z a...

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  9. Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...

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  10. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  11. Prove that the value of the determinant |[-7, 5+3i,2/3-4i], [5-3i,8, 4...

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  12. If the system of linear equation x+y+z=6,x+2y+3c=14 , and 2x+5y+lambda...

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  13. If ar=(cos2rpi+i sin 2rpi)^(19) , then prove that |[a1,a2,a3],[a4,a5,a...

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  14. Let f(x)=|(2cos^2x,sin2x,-sinx),(sin2x,2sin^2x,cosx),(sinx,-cosx,0)| ....

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  15. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

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  16. The number of positive integral solutions of the equation |(x^3+1,x^2y...

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  17. If the value of the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive...

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  18. By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,...

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  19. Using properties of determinants, evaluate |[18, 40 ,89],[ 40 ,89, 198...

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  20. If A1,B1,C1, are respectively, the cofactors of the elements a1, b1,c...

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