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For 3xx3 martrices M and N, which of the...

For `3xx3` martrices M and N, which of the following
statement (s) is (are) not correct?

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.

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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 symmetricor 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 .

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  2. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

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  3. For 3xx3 martrices M and N, which of the following statement (s) is ...

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  4. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

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  5. If A is a matrix of order mxx m such that A^(2) +A + 2I = O, then

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  6. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

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  7. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

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  8. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

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  9. A complex number U = 4+2i.The value of |U| is

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  10. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

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  11. Let A be the set of all 3xx3 symmetric matrices all of whoes entries...

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  12. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

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  13. If A is a square matrix such that A^2 = A, then write the value of (I+...

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  14. Evaluate the following determinants: {:|(3,x),(x,1)| = |(3,2),(4,1)|

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  15. If Delta={:|(1,2,3),(2,0,1),(5,3,8)|, write the minor of the element a...

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  16. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

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  17. If A = [[costheta,sintheta],[-sintheta,costheta]] then prove that A^n...

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  18. If A = {:[(cosalpha, sinalpha),(-sinalpha, cosalpha)], A'A=I.

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  19. Using elementary transformations find the inverse of [[2,0,-1],[5,1,0]...

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  20. Using properties of determinants, prove that if x, y, z are different ...

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