Home
Class 12
MATHS
If A= (a(ij)) is a 4xx4 matrix and C(ij...

If `A= (a_(ij))` is a `4xx4` matrix and `C_(ij)`, is the co-factor of the element `a_(ij)`, in `Det (A)`, then the expression `a_11C_11+a_12C_12+a_13C_13+a_14C_14` equals-

A

0

B

-1

C

1

D

Det`(A)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|26 Videos
  • MATHEMATICAL LOGIC

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTION|78 Videos
  • PAIR OF STRAIGHT LINES

    MARVEL PUBLICATION|Exercise TEST YOUR GRASP|19 Videos

Similar Questions

Explore conceptually related problems

If A=(a_(ij)) is a 4xx4 matrix and C_(ij) is the co-factor of the element a_(ij) in Det(A), then the expression a_(11)C_(11)+a_(12)C_(12)+a_(13)C_(13)+a_(14)C_(14) equals-

Let A=[a_(ij)]_(n xx n) be a square matrix and let c_(ij) be cofactor of a_(ij) in A. If C=[c_(ij)], then

If C_(ij) denotes the cofactor of the elements a_(ij) of the determinant A=|{:(2,-3,5),(6,0,4),(1,5,-7):}| then the value of a_(12)C_(12)+a_(32)C_(32) is :

If C_(ij) is the cofactor of the element a_(ij) of the determinant |{:(2,-3,5),(6,0,4),(1,5,-7):}| , then write the value of a_(32).c_(32)

If A=[a_(ij)] is a matrix of order 2xx2 , such that |A|=-15 and c_(ij) represents co-factor of a_(ij) , then find a_(21)c_(21)+a_(22)c_(22) .

Construct a 4xx3 matrix A=[a_(ij)] whose elements a_(ij) are given by: (i) a_(ij)=2i+(i)/(j)

Let A=[a_(ij)]_(3xx3) be a matrix such that a_(ij)=(i+2j)/(2) where i,j in [1, 3] and i,j inN . If C_(ij) be a cofactor of a_(ij), then the value of a_(11)C_(21)+a_(12)C_(22)+a_(13)C_(23)+a_(21)C_(31)+a_(22)C_(32)+a_(33)C_(33)+a_(31)C_(11)+a_(32)C_(12)+a_(33)C_(13) is equal to

If A=[(3,2,4),(1,2,1),(3,2,6)] and A_(ij) are the cofactors of a_(ij) , then a_(11)A_(11)+a_(12)A_(12)+a_(13)A_(13) is equal to

MARVEL PUBLICATION-MATRICES-TEST YOUR GRASP
  1. If A= (a(ij)) is a 4xx4 matrix and C(ij), is the co-factor of the ele...

    Text Solution

    |

  2. If A=[a(ij)](2xx2)" where "a(ij)=2i+j," then :"A=

    Text Solution

    |

  3. If A+3B={:[(1,2,3),(-2,3,5)]:}" and "2A+3B={:[(2,-1,4),(-1,5,2)]:}," t...

    Text Solution

    |

  4. If A and B are square matrices of order 3 such that det(A)=-2 and det(...

    Text Solution

    |

  5. If A is a non-singularmatrix such that A^(2)-A+I=O," then: "A^(-1)=

    Text Solution

    |

  6. If A=[(x,1),(1,0)] and A=A^(-1), then x= . . . .

    Text Solution

    |

  7. If AC=A" and "BA=B," then: "A^(2)=

    Text Solution

    |

  8. For a invertible matrix A if A(adjA)=[(10,0),(0,10)], then |A|=

    Text Solution

    |

  9. If A and B are square matrices of the same order such that A^(2)=A,B^(...

    Text Solution

    |

  10. If A={:[(2,3),(1,-1)]:}" and "A^(2)=A+B," then : "B=

    Text Solution

    |

  11. Solve system of linear equations, using matrix method, x y" "+" "2...

    Text Solution

    |

  12. If A={:[(1,2),(3,4)]:}," then: " adj(adjA)=

    Text Solution

    |

  13. If A={:[(4,2),(5,3)]:}" then :"|adj(adjA)|=

    Text Solution

    |

  14. If A={:[(2,-1,1),(1,2,1),(-1,1,3)]:}" then "|adj(adjA)|=

    Text Solution

    |

  15. If A={:[(secx,tanx),(tanx,secx)]:}" and "A(adj*A)=k{:[(1,0),(0,1)]:},"...

    Text Solution

    |

  16. If A=[[0,1] , [-1,0]]=(alphaI+betaA)^2 then alpha and beta =

    Text Solution

    |

  17. If A={:[(2,1),(3,2)]:}" and "B={:[(1,2),(-1,3)]:}," then: "B^(-1)A=

    Text Solution

    |

  18. If A={:[(2,3),(1,2)]:}" and "B={:[(3,1),(1,0)]:}," then: "B^(-1)A^(-1)...

    Text Solution

    |

  19. If square matrices A and B are such that A^(2)=A,B^(2)=B and A,B commu...

    Text Solution

    |

  20. If A=[a(ij)](3xx3) is a scalar matrix such that a(ij)=5" for all "i=j,...

    Text Solution

    |

  21. If A={:[(1,a),(0,1)]:}," then, for all "ninN," matrix "A^(n)=

    Text Solution

    |