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)MN` is symmetric or skew symmetric, according as M is symmetric or skew symmetric.

B

MN-NM is skew symmetric for all symmetric matrices M and N.

C

MN is symmetric for all symmetric matrices M and N.

D

(Adj M) (Adj N)=Adj(MN) for all invertible matrices M and N.

Text Solution

Verified by Experts

The correct Answer is:
C, D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2014|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2015|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE MAIN (AIEEE) ARCHIVE 2016|4 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

Similar Questions

Explore conceptually related problems

For 3xx3 matrices M \ a n d \ N , which of the following statement (s) is (are) NOT correct ? Statement - I : N^T M N is symmetric or skew-symmetric, according as M is symmetric or skew-symmetric. Statement - II : M N-N M is skew-symmetric for all symmetric matrices Ma n dN . Statement - III : M N is symmetric for all symmetric matrices M a n dN . Statement - IV : (a d jM)(a d jN)=a d j(M N) for all invertible matrices Ma n dN .

In which of the following, m gt n (m,n in R) ?

If A is a skew-symmetric matrix and n is odd positive integer, then A^n is a. a skew-symmetric matrix b. a symmetric matrix c. a diagonal matrix d. none of these

if A be a symmetric matrix then A^n will be

Let Aa n dB be two nonsingular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following options are correct? (correct option may be more than one) (a) . B^T A B is symmetric matrix (b) . if A is symmetric B^T A B is symmetric matrix (c) . if B is symmetric B^T A B is skew-symmetric matrix for every matrix A (d) . B^T A B is skew-symmetric matrix if A is skew-symmetric

If A and B are matrices of the same order, then A B^T-B A^T is a (a) skew-symmetric matrix (b) null matrix (c) unit matrix (d) symmetric matrix

If A_1, A_2, , A_(2n-1) are n skew-symmetric matrices of same order, then B=sum_(r=1)^n(2r-1)(A^(2r-1))^(2r-1) will be (a) symmetric (b) skew-symmetric (c) neither symmetric nor skew-symmetric (d)data not adequate

Let A be the set of all 3 xx 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is

Answer the following questions (Alternatives are to be noted): If X is symmetric Binomial with n = 36. Calculate E[x (x – 1)].

Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices and Z be an arbitrary 3xx3 , non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?

Home
Profile