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If the value of determinant |(a,1,1),(1,...

`If the value of determinant |(a,1,1),(1,b,1)(1,1,c)| is positive , then

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Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1],[ 1,-1,-omega^2],[omega^2, omega^2,omega]] is (a) 3omega (b) 3omega(omega-1) (c) 3omega^2 (d) 3omega(1-omega)

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CENGAGE-DETERMINANTS-All Questions
  1. Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc...

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

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

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

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  5. Using properties of determinants, evaluate |18 40 89 40 89 198 89 198 ...

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  6. if A(1) ,B(1),C(1) ……. are respectively the cofactors of the elem...

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  7. Solve for x |x-2 2x-3 3xx-4x-4 2x-9 3x-16 x-8 2x-27 3x-64|=0.

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  8. If "Delta"1=|x bb a x b a a x|a n d"Delta"2=|x b a x| are the given de...

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  9. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

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  10. if y= sin mx, them the value of the determinant |{:(y,,y(1),,y(...

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  11. Find the value of the determinant |1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20|

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  12. The parameter on which the value of the determinant |1a a^2"cos"(p-d)x...

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  13. If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r ex ,y ,z are not all zero...

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  14. If |[b^2+c^2,a b,a c],[ a b, c^2+a^2,b c],[c a, c b, a^2+b^2]|=k a^2b^...

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  15. The value of |-1 2 1 3+2sqrt(2)2+2sqrt(2)1 3-2sqrt(2)2-2sqrt(2)1| is e...

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  16. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  17. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  18. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  19. If x , y , z are in A.P. , then the value of the determinant are in A....

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  20. Prove that |((b+x)(c+x),(c+x)(a+x),(a+x)(b+x)),((b+y)(c+y),(c+y)(a+y),...

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