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

`|A|`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ML KHANNA|Exercise PROBLEM SET(1) (ASSERTION /REASON)|3 Videos

  • MATRICES

    ML KHANNA|Exercise PROBLEM SET(1) (TRUE AND FALSE)|9 Videos

  • MATRICES

    ML KHANNA|Exercise EXAMPLE|4 Videos

  • MATHEMATICAL REASONING

    ML KHANNA|Exercise PROBLEM SET (2) ASSERTION/REASON|3 Videos

  • MAXIMA AND MINIMA

    ML KHANNA|Exercise MISCELANEOUS EXERCISE (COMPREHENSION)|3 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

Construct 3xx4 matrix A=[a_(aj)] whose elements are: a_(ij)=i.j

ML KHANNA-MATRICES-PROBLEM SET(1) (MULTIPLE CHOICE QUESTIONS)
  1. If [(alpha, beta),(gamma,-alpha)] is to be square root of the two rowe...

    Text Solution

    |

  2. If A=[(a,b),(b,a)] and A^(2)=[(alpha, beta),(beta, alpha)]then (alpha,...

    Text Solution

    |

  3. If A= (a(ij)) is a 4xx4 matrix and C(ij), is the co-factor of the ele...

    Text Solution

    |

  4. If A is a square matrix such that A^(2)=A, then |A| equals

    Text Solution

    |

  5. If A^(2)+A=I then A^(-1) is

    Text Solution

    |

  6. If A^(2)-A+I=O then inverse of A is

    Text Solution

    |

  7. The multiplicative inverse of A=[(cos theta,-sin theta),(sin theta, co...

    Text Solution

    |

  8. The matrix A satisfying the equation [(1,3),(0,1)]A=[(1,1),(0,-1)] is

    Text Solution

    |

  9. If A=BX and A=[(1,2),(3,-4)] and B is [(1,0),(0,2)] then X=

    Text Solution

    |

  10. If a,b,c are non-zero real numbers, then the inverse of the matrix A=[...

    Text Solution

    |

  11. If D=diag[d(1),d(2),…………..,d(n)] where d(i)!=0AAi=1,2,3,………..n then D^...

    Text Solution

    |

  12. If A=[(3,4),(2,4)],B=[(-2,-2),(0,-2)] then (A+B)^(-1)=

    Text Solution

    |

  13. If A=diag[d(1),d(2),d(3)] then A^(n) is equal to

    Text Solution

    |

  14. Inverse of the matrix [(3,-2,-1),(-4,1,-1),(2,0,1)] is

    Text Solution

    |

  15. If A=[(1,-1,1),(2,1,-3),(1,1,1)] and 10 B=[(4,2,2),(-5,0,alpha),(1,-2,...

    Text Solution

    |

  16. The inverse of a symmetric matrix is a matrix which is

    Text Solution

    |

  17. A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] A^(-1)=1/6(...

    Text Solution

    |

  18. If A=[(0,0,1),(0,-1,0),(1,0,0)] then A^(-1)=

    Text Solution

    |

  19. Let F(alpha)=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,...

    Text Solution

    |

  20. If E(theta)=[(cos theta, sin theta),(-sin theta, cos theta)], then E(a...

    Text Solution

    |