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If A is a symmetric and B skew symmetric...

If A is a symmetric and B skew symmetric matrix and `(A+ B)` is non-singular and `C = (A+B)^-1 (A-B)`, then prove that

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Knowledge Check

  • If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

    A
    `A + B`
    B
    `A-B`
    C
    A
    D
    B

  • If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) , C^(T)(A+B)C equals to

    A
    `A + B`
    B
    `A-B`
    C
    A
    D
    B

  • If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

    A
    `[{:(-4,-2),(-1,4):}]`
    B
    `[{:(4,-2),(-1,-4):}]`
    C
    `[{:(4,-2),(1,-4):}]`
    D
    `[{:(-4,2),(1,4):}]`

    • Similar Questions

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    If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

    If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [{:(2,3),(5,-1):}] , then AB is equal to

    If A and B are symmetric non singular matrices, AB = BA and A^(-1) B^(-1) exist, then prove that A^(-1)B^(-1) is symmetric.

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

    If A= B+C such that B is a symmetric matrix and C is a skew - symmetric matrix , then B is given by :

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