Home
Class 12
MATHS
Delta= [[ 1 / a , 1 , b c ],[1 / b , 1 ...

`Delta= [[ 1 / a , 1 , b c ],[1 / b , 1 , c a ],[1 / c , 1 , a b]] =`

A

0

B

abc

C

`(1)/(a b c)`

D

`a^2 b^2 c^2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

  • MAXIMA AND MINIMA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

|[1, a, a^2-b c],[1,b, b^2-c a],[1,c, c^2-a b]|=

With the usual notation in the triangle A B C [[ 1 , 1 , 1 ],[ sin A , sin B , sin C ],[ sin ^2 A , sin ^2 B , sin ^3 C ]] =

The inverse of the matrix [[1 , 0, 0],[ a , 1 , 0],[ b, c , 1]] is

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

If D=[[1,a,b],[1,b,c],[1,c,a]] , then [[a,b,c],[b,c,a],[1,1,1]] =

If (1)/(a)+(1)/(b)+(1)/(c)=0 then |[1+a, 1, 1 ],[1, 1+b, 1],[1,1,1+c]| =

If a, b, c are all different from zero and Delta= |[1+a,1,1],[1,1+b,1],[1,1, 1+c]|=0 , then (1)/(a)+(1)/(b)+(1)/(c)=

Show that |(1+a,1,1),(1,1+b,1),(1,1,1+c)| = abc(1 + 1/a + 1/b + 1/c) = abc + bc + ca + ab .

Show that {:|( 1+a,1,1),( 1,1+b,1) ,( 1,1,1+c) |:}= abc ( 1+(1)/(a) +(1)/(b) +(1)/(c) ) = abc +bc +ca +ab

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. If A= [[-1 , 2 , 4 ],[ 3 , 1 , 0],[ -2 , 4 , 2 ]] and B= [[-2 , 4 ...

    Text Solution

    |

  2. If [[ a , b , c],[ m , n , p],[ x , y , z ]] =k, then [[ 6 a , 2 b ,...

    Text Solution

    |

  3. Delta= [[ 1 / a , 1 , b c ],[1 / b , 1 , c a ],[1 / c , 1 , a b]] =

    Text Solution

    |

  4. If [[ x , 2 , x],[x^2 , x , 6],[x , x , 6 ]] =a x^4+b x^3+c x^2+d x+e,...

    Text Solution

    |

  5. If omega is an imaginary cube root of unity then the value of [[1+ome...

    Text Solution

    |

  6. If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of...

    Text Solution

    |

  7. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

    Text Solution

    |

  8. The value of determinant |(a-b ,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is

    Text Solution

    |

  9. If [[ 2 x , 5],[ 8 , x ]] = [[6 , -2 ],[7 , 3 ]], then, x=

    Text Solution

    |

  10. The number of distinct real roots of [[sin x , cos x , cos x ],[cos x ...

    Text Solution

    |

  11. There are two values of a which makes determinant , A=|(1,-2,5),(2,a,-...

    Text Solution

    |

  12. The value of determinant |(x,x+y,x+2y),(x+2y,x,x+y),(x+y,x+2y,x)| is

    Text Solution

    |

  13. If x, y, z are all different and not equal to zero and |{:(1+x,,1,,...

    Text Solution

    |

  14. If A = [ (2,lambda,-3),(0,2,5),(0,1,3)] , then A^(-1) exists if :

    Text Solution

    |

  15. A root of the equation |(0, x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 is

    Text Solution

    |

  16. The maximum value of Delta=|(1,1,1),(1,1+sintheta,1),(1+costheta,1,1)|...

    Text Solution

    |

  17. Let f(t)=|(cost,t,1),(2sint,t,2r),(sint,t,t)| , then {:(lim),(t rarr0)...

    Text Solution

    |

  18. If A,B and C are angles of a triangle, then the determinant : |(-1,c...

    Text Solution

    |

  19. If A is a square matrix of order 3 xx 3, then |KA| is equal to

    Text Solution

    |

  20. Which of the following is correct

    Text Solution

    |