Home
Class 12
MATHS
A is a skew-symmetric of order 3, wri...

`A` is a skew-symmetric of order 3, write the value of `|A|` .

Text Solution

Verified by Experts

Since A is a skew-symmetric matrix,
Therefore `A^T = -A`
Taking determinant both sides
`|A^T| = |-A|`
Using `|A^T| = |A|`
and `|λA| = λ^m|A|`
where m is the order of `A |A| = (-1)^3|A| = -|A| or 2|A| = 0`
Hence, `|A| = 0`
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos
  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

If A is a skew-symmetric matrix of order 3 , then find the value of |A| .

If A is skew symmetric matrix of order 3 then the value of |A| is

If A is a skew-symmetric matrix of order 3, then |A|=

If A is a skew-symmetric matrix of order n, then the maximum number of no-zero elements in A is

If A is a skew-symmetric matrix of order 3 then A^(3) is

If A is a skew-symmetric matrix of order 3, then prove that det A=0.

If A=[a_(ij)] is a skew-symmetric matrix,then write the value of sum_(i)a_(ii)

If A=[a_(ij)] is a skew-symmetric matrix,then write the value of sum_(i)sum_(j)a_(ij)

If A=[a_(ij)] is a skew-symmetric matrix,then write the value of sum_(i)a_(ij).

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If A is a square matrix of order n and A A^T = I then find |A|

    Text Solution

    |

  2. If A and B are square matrices of the same order such that |A|=3 an...

    Text Solution

    |

  3. A is a skew-symmetric of order 3, write the value of |A| .

    Text Solution

    |

  4. If A is a square matrix of order 3 with determinant 4, then write t...

    Text Solution

    |

  5. If A is a square matrix such that |A|=2 , write the value of |AA^T|

    Text Solution

    |

  6. Find the value of determinant |243 156 300 81 52 100-3 0 4| .

    Text Solution

    |

  7. Write the value of the determinant |2-3 5 4-6 10 6-9 15| .

    Text Solution

    |

  8. If the matrix [5x2-10 1] is singular, find the value of x .

    Text Solution

    |

  9. If A is a square matrix of order nxxn such that |A|=lambda , then w...

    Text Solution

    |

  10. Find the value of the determinant |2^2 2^3 2^4 2^3 2^4 2^5 2^4 2^5 ...

    Text Solution

    |

  11. If A and B are non-singular matrices of the same order, write wheth...

    Text Solution

    |

  12. A matrix of order 3xx3 has determinant 2. What is the value of |A(3...

    Text Solution

    |

  13. If A and B are square matrices of order 3 such that |A|=-1 , |B|=3 ...

    Text Solution

    |

  14. Write the value of |a+i b c+i d-c+i d a-i b| .

    Text Solution

    |

  15. Write the cofactor of a(12) in the matrix [2-3 5 6 0 4 1 5-7]

    Text Solution

    |

  16. If |[2x+5, 3], [5x+2, 9]|=0 , find xdot

    Text Solution

    |

  17. Find the value of x from the following: |[x,4], [2, 2x]|=0

    Text Solution

    |

  18. Write the value of the determinant |A|=|[2,3,4],[5,6,8],[6x,9x,12x]|

    Text Solution

    |

  19. If |A|=2 , where A is 2xx2 matrix, find |a d j\ A| .

    Text Solution

    |

  20. What is the value of the determinant |[0, 2, 0],[ 2, 3, 4],[ 4 ,5 ,...

    Text Solution

    |