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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 a symmetric or skew symmetricm according as M is symmetric or skew symmetric

B

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

C

M N is symmetric for al symmetric matrices M and N

D

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

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The correct Answer is:
C, D
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RESONANCE-MATRICES & DETERMINANT-EXERCISE-3
  1. Let a, b and c be three real number satisfying [a,b,c]|{:(,1,9,7),(,...

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  2. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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

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  4. Let P=[a]"be a "3xx3 matrix and let Q=[b]=2^(i+j)a(i) "for" 1 lei, j l...

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

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  6. If the adjoint of a 3 xx 3 matrix P is [{:(,1,4,4),(,2,1,7),(,1,1,3):}...

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

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  8. Let M be a 2 x 2 symmetric matrix with integer entries . Then , ...

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  9. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

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

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  11. Which of the following values of alpha satisfying the equation |(1+alp...

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

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  13. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

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

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  15. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

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  16. Which of the following is (are) NOT the square of a 3xx3 matrix with r...

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

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

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  19. Let S be the set of all column matrices [(b(1)), (b(2)), (b(3))] such ...

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

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