Home
Class 12
MATHS
Express the matrix A=[4 2-1 3 5 7 1-2 1]...

Express the matrix `A=[4 2-1 3 5 7 1-2 1]` as the sum of a symmetric and a skew-symmetric matrix.

Text Solution

Verified by Experts

Given,
`A=[[4,2,-1],[3,5,7],[1,-2,1]]`
Then,
`A^T=[[4,3,1],[2,5,-2],[-1,7,1]]`
`X=1/2*(A=A^T)`
`=1/2([[4,2,-1],[3,5,7],[1,-2,1]]+[[4,3,1],[2,5,-2],[-1,7,1]])`
`=1/2[[8,5,0],[5,10,5],[0,5,2]]`
`X=[[4,5/2,0],[5/2,5,5/2],[0,5/2,1]]`
...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

Express the matrix B=[2,-2,-4-1,3,41,-2,-3] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A=[323453245] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix A=[3-41-1] as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix [ 2 0 −4 6 −2 2 0 8 4 ] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A=[{:(2,3),(-1,4):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

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

Express the matrix A=[{:(3,-4),(1,-1):}] as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix B= [{:(,2,-2,),(,-1,3,):}] as the sum of a symmetric and a skew symmetric matrix.

Express the matrix A=[[3,1,4] , [0,2,6] , [0,0,5]] as the sum of symmetric and skew-symmetric matrix

Express the matrix A=[[3,1,4] , [0,2,6] , [0,0,5]] as the sum of symmetric and skew-symmetric matrix

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If the matrix A=[5 2x y z-3 4t-7] is a symmetric matrix, find x ,\ y ,...

    Text Solution

    |

  2. Let A=[3 2 7 1 4 3-2 5 8] . Find matrices X and Y such that X+Y=A , wh...

    Text Solution

    |

  3. Express the matrix A=[4 2-1 3 5 7 1-2 1] as the sum of a symmetric and...

    Text Solution

    |

  4. Define a symmetric matrix. Prove that for A=[2 4 5 6] , A+A^T is a ...

    Text Solution

    |

  5. Express the matrix A=[3-4 1-1] as the sum of a symmetric and a skew-sy...

    Text Solution

    |

  6. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

    Text Solution

    |

  7. If A is an mxxn matrix and B is nxxp matrix does A B exist? If yes, wr...

    Text Solution

    |

  8. If A=[2 1 4 4 1 5] and B=[3-1 2 2 1 3] . Write the orders of A B and B...

    Text Solution

    |

  9. If A=[4 3 1 2] and B=[-4 3] , write A B .

    Text Solution

    |

  10. If A=[1 2 3] , write AA^T .

    Text Solution

    |

  11. Give an example of two non-zero 2xx2 matrices A and B such that A B...

    Text Solution

    |

  12. If A=[2 3 5 7] , find A+A^T .

    Text Solution

    |

  13. If A=[i0 0i] , write A^2 .

    Text Solution

    |

  14. If A=[(cosx,sinx),(-sinx,cosx)] , find x satisfying 0<x<pi/2 when A+A^...

    Text Solution

    |

  15. If A=[(cosx,-sinx),(sinx,cosx)] , find AA^T

    Text Solution

    |

  16. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

    Text Solution

    |

  17. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

    Text Solution

    |

  18. If A=[1 1 1 1] satisfies A^4=lambdaA , then write the value of lambda

    Text Solution

    |

  19. If A=[-1 0 0 0-1 0 0 0-1] , find A^2 .

    Text Solution

    |

  20. If A=[-1 0 0 0-1 0 0 0-1] , find A^3 .

    Text Solution

    |