Home
Class 12
MATHS
Delta=|(a(11),a(12),a(13)),(a(21),a(22),...

`Delta=|(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))| and A_(ij)` is cofactor of `a_(ij)` then value of `Delta` is given by

A

`a_(11)+A_(31)+a_(12)A_(32)+a_(13)A_(33)`

B

`a_(11)+A_(11)+a_(12)A_(21)+a_(13)A_(31)`

C

`a_(21)+A_(11)+a_(22)A_(12)+a_(23)A_(13)`

D

`a_(11)+A_(11)+a_(21)A_(21)+a_(31)A_(31)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-II (Fill in the blanks questions)|31 Videos

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Type-III (True or False questions)|25 Videos

  • DETERMINANTS

    ACCURATE PUBLICATION|Exercise Example (Questions caryying 6 marks)|35 Videos

  • DEFINITE INTEGRALS

    ACCURATE PUBLICATION|Exercise QUESTION CARRYING 4 MARKS|8 Videos

  • DIFFERENTAL QUATIONS

    ACCURATE PUBLICATION|Exercise QUESTIONS CARRYING 4 MARKS|41 Videos

Similar Questions

Explore conceptually related problems

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| then cofactor of a_23 represented as

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). Suppose a,b,c, in R, a+b+c gt 0, A =bc -a^(2),B =ca-b^(2) and c=ab-c^(2) and |{:(A,B,C),(B,C,A),(C,A,B):}| =49 then the valu of a^(3)+b^(3)+c^(3) -3abc is

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 Let d_(i) be the common difference of the elements in with row then sum_(i=1)^(n)d_(i) is

Let A be nxxn matrix given by A=[(a_(11),a_(12),a_(13)……a_(1n)),(a_(21),a_(22),a_(23)…a_(2n)),(vdots, vdots, vdots),(a_(n1),a_(n2),a_(n3).a_("nn"))] Such that each horizontal row is arithmetic progression and each vertical column is a geometrical progression. It is known that each column in geometric progression have the same common ratio. Given that a_(24)=1,a_(42)=1/8 and a_(43)=3/16 .Let Di be the common difference of i^(th) row The value of lim_(nto oo)sum_(i=1)^(n)D_(i) is equal to

If (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

If A=[a_(ij)]_(2×3) such that a_(ij)=i+j then a 11=

Statement-1: If f:{a_(1),a_(2),a_(3),a_(4),a_(5)}to{a_(1),a_(2),a_(3),a_(4),a_(5)} , f is onto and f(x)nex for each x in{a_(1),a_(2),a_(3),a_(4),a_(5)} , is equal to 44. Statement-2: The number of derangement for n objects is n! sum_(r=0)^(n)((-1)^(r))/(r!) .

ACCURATE PUBLICATION-DETERMINANTS-Type-I (Multiple choice questions)
  1. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

    Text Solution

    |

  2. If area of triangle is 4 sq. units with vertices (-2, 0), (0, 4) and (...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If A is a non-singular matrix of order 3 and |A| = 3, then |Adj. A| eq...

    Text Solution

    |

  7. If A is a non-singular matrix of order 3 and |A| = 2, then | adj A| eq...

    Text Solution

    |

  8. If A is a non-singular matrix of order 3 and |A| = 4, then |Adj. A| eq...

    Text Solution

    |

  9. If A is an invertible square matrix of order 4, then |adj. A| is equal...

    Text Solution

    |

  10. If A is non-singular matrix of order 3 and |A|=5 then |adj.A| equals :

    Text Solution

    |

  11. If A is a matrix of order 3xx3 and abs (A) = 10 then abs (adj. A) is

    Text Solution

    |

  12. If A is a square matrix of order 3xx3 and abs(A) = 5 then abs (Adj. A)...

    Text Solution

    |

  13. If A = ([2,1],[1,2]), then A (Adj A) equals :

    Text Solution

    |

  14. If A=[{:(3,1),(1,2):}], then A(adjA) equals

    Text Solution

    |

  15. If A = ([4,3],[3,4]), then A (Adj A) equals :

    Text Solution

    |

  16. If A=[(3,2),(1,4)] , then A(adj A) equals

    Text Solution

    |

  17. The inverse of a symmetric matrix is :

    Text Solution

    |

  18. Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

    Text Solution

    |

  19. If x,y in R then the determinant Delta=|{:(cosx,-sinx,1),(sinx,cosx,1)...

    Text Solution

    |

  20. If |(2x,5),(8,x)|=|(6,-2),(7,3)| , write the value of x.

    Text Solution

    |