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

If the value of the determinant `|(a,1, 1) (1,b,1) (1,1,c)|` is positive then a. `a b c >1` b. `a b c> -8` c.`a b c<-8` d. `a b c > -2`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

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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 the determinant |(a,1, 1) (1,b,1) (1,1,c)| is positive...

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

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

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

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

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  8. If Delta1=|[x, b, b],[ a, x, b],[ a, a, x]| a n d Delta2=|[x, b],[ a, ...

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

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  10. If y= sin px and y(n) is the nth derivative of y, then |{:(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, ...

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  12. The parameter on which the value of the determinant |1 a...

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

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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...

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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. If |[1 1 1];[a b c];[ a^3b^3c^3]|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b...

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  19. 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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  20. The determinant |[y^2,-x y, x^2],[a, b, c],[ a ', b ', c ']| is equal ...

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