Home
Class 12
MATHS
For 3xx3 matrices Ma n dN , which of the...

For `3xx3` matrices `Ma n dN ,` which of the following statement (s) is (are) NOT correct ? `N^T M N` is symmetricor skew-symmetric, according as `m` is symmetric or skew-symmetric. `M N-N M` is skew-symmetric for all symmetric matrices `Ma n dNdot` `M N` is symmetric for all symmetric matrices `M a n dN` `(a d jM)(a d jN)=a d j(M N)` for all invertible matrices `Ma n dNdot`

A

`N^(T)M` N is symmetric or skew symmetric, according as M is symmetric or skew symmetric

B

M N – N M is skew symmetric for all symmetric matrices M and N

C

M N is symmetric for all symmetric matrices M and N

D

(adj M) (adj N) = adj (M N) for all invertible matrices M and N

Text Solution

Verified by Experts

The correct Answer is:
C, D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-I)|19 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

For 3 xx 3 matrices M and N, which of the following statement(s) is/are not correct?

If A is a symmetric matrix and n in N, write whether A^(n) is symmetric or skew-symmetric or neither of these two.

If A is a symmetric matrix and n in N, write whether A^(n) is symmetric or skew-symmetric or neither of these two.

If A is a symmetric matrix and n in N then A^(n) is

If A and B are symmetric matrices of the same order then (A) A-B is skew symmetric (B) A+B is symmetric (C) AB-BA is skew symmetric (D) AB+BA is symmetric

If A is a skew-symmetric matrix and n is odd positive integer,then A^(n) is a skew-symmetric matrix a symmetric matrix a diagonal matrix none of these

If A and B are symmetric matrices,then ABA is (a) symmetric matric b) skew-symmetric matrix (c) diagonal matrix (d) scalar matrix

Which of the following statement is incorrect? Statement I: If A and B are symmetric matrices of order n, then AB+BA is symmetricand AB - BA is skew symmetric Statement Ill: |adj(adjA)|=|A|^((n-1)^(2))

express the following matrices as a sum of symmetric and skew symmetric matrices : (i) [{:(3,-7),(4,2):}]

MOTION-MATRICES -Exercise - 4 (Level-II)
  1. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  2. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  3. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  4. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  5. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  6. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

    Text Solution

    |

  7. Let M be a 3xx3 matrix satisfying M[{:(0),(1),(0):}]=[{:(-1),(2),(3):}...

    Text Solution

    |

  8. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

    Text Solution

    |

  9. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  10. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

    Text Solution

    |

  11. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  12. Let Ma n dN be two 3xx3 matrices such that M N=N Mdot Further, if M!=N...

    Text Solution

    |

  13. Let M be a 2 × 2 symmetric matrix with integer entries. Them M is inve...

    Text Solution

    |

  14. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

    Text Solution

    |

  15. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  16. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

    Text Solution

    |

  17. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

    Text Solution

    |

  18. Which of the following is (are) NOT the square of a 3 xx 3 matrix with...

    Text Solution

    |

  19. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

    Text Solution

    |

  20. Let P be a matrix of order 3xx3 such that all the entries in P a...

    Text Solution

    |