Home
Class 12
MATHS
If A is symmetric and B skew- symmetric ...

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

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `A^(T) = A, B^(T) = -B, det (A+ B) ne 0`
and `C = (A + B)^(-1) (A-B)`
`rArr (A + B) C = A - B` ...(i)
Also, ` (A + B) ^(T)= A - B` ...(ii)
and ` (A - B) ^(T)= A + B` ...(iii)
`C^(T) AC = C^(T)((A+B +A-B)/2) C`
`= 1/2 C^(T) (A + B) C+ 1/2 C^(T) (A-B) C`
`= 1/2 (A + B) + 1/2 (A-B) `
`=A`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Matrices Exercise 5 : (Matching Type Questions )|4 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

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

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

If A is a symmetric and B skew symmetric matrix and (A+B) si non-singular and C=(A+B)^(-1)(A-B) , then prove that. (i) C^(T)(A+B)C=A+B (ii) C^(T)(A-B)C=A-B

If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsingular and C=(A+B)^(-1) (A-B) , then prove that (i) C^(T) (A+B) C=A+B (ii) C^(T) (A-B)C=A-B (iii) C^(T)AC=A

If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

A is said to be skew-symmetric matrix if A^(T) = a)A b)-A c) A^2 d) A^3

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 skew symmetric matrix of order n and C is a column matrix of order nxx1 , then C^(T)AC is

ARIHANT MATHS-MATRICES -Exercise (Passage Based Questions)
  1. Suppose A and B be two ono-singular matrices such that AB= BA^(m), B...

    Text Solution

    |

  2. Suppose A and B be two ono-singular matrices such that AB= BA^(m), B...

    Text Solution

    |

  3. Suppose A and B be two ono-singular matrices such that AB= BA^(m), B...

    Text Solution

    |

  4. Let A= [[a,b,c],[b,c,a],[c,a,b]] is an orthogonal matrix and abc = lam...

    Text Solution

    |

  5. Let A= [[a,b,c],[b,c,a],[c,a,b]] is an orthogonal matrix and abc = lam...

    Text Solution

    |

  6. Let A= [[a,b,c],[b,c,a],[c,a,b]] is an orthogonal matrix and abc = lam...

    Text Solution

    |

  7. LatA = [a(ij)](3xx 3). If tr is arithmetic mean of elements of rth row...

    Text Solution

    |

  8. LatA = [a(ij)](3xx 3). If tr is arithmetic mean of elements of rth row...

    Text Solution

    |

  9. LetA= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C(1), C(2), C(...

    Text Solution

    |

  10. LetA= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C(1), C(2), C(...

    Text Solution

    |

  11. LetA= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C(1), C(2), C(...

    Text Solution

    |

  12. If A is symmetric and B skew- symmetric matrix and A + B is non-sing...

    Text Solution

    |

  13. If A is a symmetric and B skew symmetric matrix and (A+ B) is non-sing...

    Text Solution

    |

  14. If A is symmetric and B skew- symmetric matrix and A + B is non-sin...

    Text Solution

    |

  15. Let A be a squarre matrix of order of order 3 satisfies the matrix equ...

    Text Solution

    |

  16. Let A be a squarre matrix of order of order 3 satisfies the matrix equ...

    Text Solution

    |