Home
Class 12
MATHS
Consider the following statements : (a...

Consider the following statements :
(a) If any two rows or columns of a determinant are identical, then the value of the determinant is zero
(b) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change.
(c) If any two rows or columns of a determinant are interchanged, then the value of the determinant changes in sign.
Which of these are correct ?

A

(a) and ©

B

(a) and (b)

C

(a), (b) and ©

D

(b) and ©

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|272 Videos

  • COMMON ENTRANCE TEST - 2017

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos

Similar Questions

Explore conceptually related problems

Consider the following statements : (i) If any two rows or columns of a determinant are identical, then the value of the determinant is zero. (ii) If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change. (iii) If any two rows ( or columns) of a determinant are interchanged , then the value of the determinant changes in sign. Which of these are correct ?

If any two rows (or columns) of a determinant are identical then the value of the determinants is 0.

If any two rows (or columns) of a determinant are interchanged then the sign of a determinant changes.

Prove that the value of the determine remains unchanged if its rows and columns are interchanged.

ZO-ZZ type of sex determination is

Prove that if each element of a row (or a column) of a determinant is multiplied by k, then its value gets multiplied by k.

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its elements by its cofactor is

How emf of a cell is determined ?

HIMALAYA PUBLICATION-COMMON ENTRANCE TEST - 2014-QUESTION BANK
  1. The symmetric part of the matrix A = ((1,2,4),(6,8,2),(2,-2,7)) is

    Text Solution

    |

  2. If A is a matrix of order 3, such that A(adj A) = 101, then |adj A| =

    Text Solution

    |

  3. Consider the following statements : (a) If any two rows or columns o...

    Text Solution

    |

  4. The inverse of the matrix A=[(2,0,0),(0,3,0),(0,0,4)] is

    Text Solution

    |

  5. If a, b and c are in A.P., then the value of |(x+2, x+3, x+a),(x+4, x+...

    Text Solution

    |

  6. The local minimum value of the function f' given by f(x) = 3 + |x|, x ...

    Text Solution

    |

  7. A stone is dropped into a quiet lake and waves move in circles at the ...

    Text Solution

    |

  8. A gardener is digging a plot of land. As he gets tired, he works more ...

    Text Solution

    |

  9. The area of the region bounded by the lines y=mx, x =1, x=2, and x axi...

    Text Solution

    |

  10. Area of the region bounded by two parabolas y = x^(2) and x = y^(2) is

    Text Solution

    |

  11. The order and degree of the differential equation y = x(dy)/(dx) + (2)...

    Text Solution

    |

  12. The general solution of the differential equation (dy)/(dx)+y/x=3x is

    Text Solution

    |

  13. The distance of the point P(a, b, c) from the x-axis is

    Text Solution

    |

  14. Equation of the plane perpendicular to the line x/1=y/2=z/3 and passin...

    Text Solution

    |

  15. The line (x-2)/(3) = (y-3)/(4) = (z-4)/(5) is parallel to the plane

    Text Solution

    |

  16. The angle between two diagonals of a cube is

    Text Solution

    |

  17. The lines : (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k =(y-4)/2 =(z-5)/1 a...

    Text Solution

    |

  18. A and B are two events such that P(A)!=0, P(B//A) is

    Text Solution

    |

  19. Two dice are thrown simultaneously. The probability of obtaining a tot...

    Text Solution

    |

  20. If the events A and B are independent if P(A')=2/3 and P(B')=2/7, then...

    Text Solution

    |