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If x,y,z are different and Delta= {:|(x,...

If x,y,z are different and `Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0`, show that xyz=-1

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If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

Prove that: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+z)

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 then using properties of determinants, show that xyz= -1.

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

OMEGA PUBLICATION-DETERMINANTS-Multiple Choice Questions (MCQs)
  1. If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

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  2. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  3. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  4. If A is an invertible matrix of order n, then |adj A|=

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  5. If area of triangle is 35 sq. units with vertices (2, - 6), (5, 4) and...

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  6. Delta=|(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33))| an...

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  7. Let A be a non-singular matrix of order 3 xx 3. Then I adj. A I is equ...

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  8. Select the Correct Option If A is an invertible matrix of order 2, the...

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  9. If a, b, c are in A.P., then the determinant abs{:(x+2, x+3, x+2a),(x+...

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  10. If x, y, z are non-zero real numbers, then the inverse of matrix A = [...

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  11. Let A = [{:(1, sin theta , 1),(-sin theta, 1 , sin theta),(-1 , - sin ...

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  12. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

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  13. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  14. If A is an invertible matrix of order n, then |adj A|=

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  15. If area of triangle is 35 sq. units with vertices (2, - 6), (5, 4) and...

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  16. Delta=|(a(11),a(12),a(13)),(a(21),a(22),a(23)),(a(31),a(32),a(33))| an...

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  17. Let A be a non-singular square matrix of order 3×3. Then abs(adjA) is

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  18. lf A is an invertible matrix of order 2, then |A^(-1) | is equal to

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  19. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

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  20. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

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  21. Let A = [{:(1, sin theta , 1),(-sin theta, 1 , sin theta),(-1 , - sin ...

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