Home
Class 12
MATHS
Let A = (a(ij)(3xx3) be a matrix with a(...

Let A = `(a_(ij)_(3xx3)` be a matrix with `a_(ij ) in C`. Let B be a matrix obtained by inerchanging two columns of A . Then det (A+B) is equal to

A

det (A) +det (B)

B

0

C

2 det (A)

D

det( A) - det(B)

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE ( LEVEL -2 ) ( single Correct Answer Type Questions)|17 Videos
  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Numerical Answer Type Questions)|20 Videos
  • MATRICES

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Concept - based) (Single Correct Answer Type Questions)|10 Videos
  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos
  • PARABOLA

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTRE ENTRANCE EXAMINATION PAPERS|9 Videos

Similar Questions

Explore conceptually related problems

Let A = (a_(ij)_(3xx2) be a 3xx2 matrix with real entries and B = AA. Then

A matrix A=[a_(ij)] is an upper triangular matrix, if

Let A=[a_(ij)]_(3xx3) be a scalar matrix and a_(11)+a_(22)+a_(33)=15 then write matrix A.

A matrix A=[a_(ij)]_(mxxn) is

If A=[a_(ij)]_(2xx3) , difined as a_(ij)=i^(2)-j+1 , then find matrix A.

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

Let A = [a_(ij)] " be a " 3 xx3 matrix and let A_(1) denote the matrix of the cofactors of elements of matrix A and A_(2) be the matrix of cofactors of elements of matrix A_(1) and so on. If A_(n) denote the matrix of cofactros of elements of matrix A_(n -1) , then |A_(n)| equals

Let A=[a_("ij")]_(3xx3), B=[b_("ij")]_(3xx3) and C=[c_("ij")]_(3xx3) be any three matrices, where b_("ij")=3^(i-j) a_("ij") and c_("ij")=4^(i-j) b_("ij") . If det. A=2 , then det. (BC) is equal to _______ .

If A=[a_(ij)]_(3xx3) is a scalar matrix such that a_(ij)=5" for all "i=j," then: "|A|=

MCGROW HILL PUBLICATION-MATRICES-EXERCISE ( LEVEL -1) (Single Correct Answer Type Questions)
  1. Let S be the set of all 2xx2 real matrices A = [(a,b),(c,d)] such that...

    Text Solution

    |

  2. Let A = (a(ij)(3xx2) be a 3xx2 matrix with real entries and B = AA. T...

    Text Solution

    |

  3. Let A = (a(ij)(3xx3) be a matrix with a(ij ) in C. Let B be a matrix o...

    Text Solution

    |

  4. If I = ((1,0),(0,1)), J = ((0,1),(-1,0)) and B = ((cos theta , sin the...

    Text Solution

    |

  5. If A is both diagonal and skew - symmetric then

    Text Solution

    |

  6. If A^(2) - 3A +2I =0 then A^(-1) equals

    Text Solution

    |

  7. If A is a square matrix of order 3 such that A^(2) = 2A then |A|^(2) ...

    Text Solution

    |

  8. If A is a squyare matrix then which one of the following is not a symm...

    Text Solution

    |

  9. If A = (a(ij))(3xx3) where a(ij) = cos (i+j) then

    Text Solution

    |

  10. If A = (a(ij))(3xx) is a matrix satrisfying the equation x^(3) -3x+1 =...

    Text Solution

    |

  11. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

    Text Solution

    |

  12. If [(I,0),(3,-i)]+X = [(I,2),(3,4+i)] -X then X is equal to

    Text Solution

    |

  13. If A = [(0,-i),(i,0)] B = [(1,0),(0,-1)] then A B+ BA is

    Text Solution

    |

  14. A =[(1,2,3),(1,2,3),(-1,-2,-3)] then A is a nilpotent matrix of index

    Text Solution

    |

  15. If A is a 2xx2 unitary matrix then |A| is equal to

    Text Solution

    |

  16. If A= (1)/(2) ((-1,-sqrt(3)),(sqrt(3),-1)) then A^(-1)- A^(2) is equal...

    Text Solution

    |

  17. If C is a 3xx3 matrix satisfying the relation C^(2)+C=I then C^(-2) is...

    Text Solution

    |

  18. If A , B and C are three square matrices of the same size such that B ...

    Text Solution

    |

  19. If X is a 2 xx 3 matrix such that |X' X|!=0 and A = I2 - X(X' X)^(-1) ...

    Text Solution

    |

  20. The matrix A =((p,-q),(q,p)) is orthogonal if and only if

    Text Solution

    |