Home
Class 12
MATHS
For the matrixA=[[1,5],[6,7]], verify th...

For the matrix`A=[[1,5],[6,7]]`, verify that
`A-A^T` is a skew symmetric matrix

Text Solution

Verified by Experts

`A-A^T = [(0,-1),(1,0)] implies (A+A^T)^T = [(0,1),(-1,0)] = -(A-A^T)`
`therefore `A-A^T` is skew symmetric
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|40 Videos
  • PROBABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|318 Videos

Similar Questions

Explore conceptually related problems

For the matrix A=[[1,5],[6,7]] , verify that A+A^T is a symmetric matrix

For the matrix A=[[1 , 5],[ 6 , 7]] , verify that i) (A+A^') is a symmetric matrix. ii) (A-A') , is a skew symmetric matrix.

For the matrix A=[[2,4],[5,6]] , verify that A+A^T is a symmetric matrix.

show that the matrix A= [[0,1,-1],[-1,0,1],[1,-1,0]] is a skew symmetric matrix

Let A be a square matrix. Then prove that A - A^(T) is a skew-symmetric matrix

Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric matrix.

If A and B are symmetric matrices, prove that A B-B A is a skew symmetric matrix.

Consider the matrix A=[[2,5],[3,2]] Find A^-1

For any square matrix A with real number entries.Prove that A+A^' is a symmetric matrix and A-A^' is a skew symmetric matrix.

From the symmetric matrix A=[(2,x,4),(5,3,8),(4,y,9)] , verify AA' and A+A' are symmetric matrices.

A N EXCEL PUBLICATION-MATRICES-QUESTION BANK
  1. show that the matrix A=[[0,1,-1],[-1,0,1],[1,-1,0]] is a skew symmetri...

    Text Solution

    |

  2. For the matrixA=[[1,5],[6,7]], verify that A+A^T is a symmetric matr...

    Text Solution

    |

  3. For the matrixA=[[1,5],[6,7]], verify that A-A^T is a skew symmetric...

    Text Solution

    |

  4. Find 1/2 (A+A^T) and 1/2(A-A^T) where A=[[0,a,b],[-a,0,c],[-b,-c,0]]

    Text Solution

    |

  5. Write A=[[3,5],[1,-1]] as the sum of a symmetric and a skew symmetric ...

    Text Solution

    |

  6. Express the following matrices as the sum of a Symmetric and a Skew Sy...

    Text Solution

    |

  7. Express the following matrices as the sum of a Symmetric and a Skew Sy...

    Text Solution

    |

  8. Express the following matrics as the sum of a symmetrics and a skew sy...

    Text Solution

    |

  9. If A,B are symmetric matrices of same order then AB-BA is always a ………...

    Text Solution

    |

  10. If A=[[cos alpha, -sin alpha],[sin alpha, cos alpha]], then A+A^T=I if...

    Text Solution

    |

  11. Find P^(-1), if it exists, given P = [(10,-2),(-5,1)]

    Text Solution

    |

  12. Using elementry transformation, find the inverse of the matrices. Co...

    Text Solution

    |

  13. Using elementary transformation find the inverse of the matrix [[2,1]...

    Text Solution

    |

  14. Using elementry transformation, find the inverse of the matrices. A=...

    Text Solution

    |

  15. Find the inverse of the following using elementary transformations. A=...

    Text Solution

    |

  16. Find the inverse of the following using elementary transformations. A=...

    Text Solution

    |

  17. Find the inverse of the following using elementary transformations. A=...

    Text Solution

    |

  18. Find the inverse of the following using elementary transformations. A=...

    Text Solution

    |

  19. Using elementry transformation, find the inverse of the matrices. A ...

    Text Solution

    |

  20. Using elementry transformation, find the inverse of the matrices. A ...

    Text Solution

    |