InterviewSolution
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InterviewSolution
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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 allsymmetric matrices `Ma n dNdot``M N`is symmetric for all symmetricmatrices `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 of skew-symmetricB. `MN-NM` is skew-symmetric for all symmetric matrices M and NC. MN is symmetric for all symmetric matrices M and ND. (adj M) (adj N) = adj (MN) for all invertible matrices M and N |
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Answer» Correct Answer - C::D (a) `(N^(T) MN)^(T) = N^(T) M^(T) (N^(T))^(T)=N^(T)M^(T)N=N^(T) MN` or `-N^(T) MN` According as M is symmetric ro skew-symmetric. `therefore` Correct. (b) `(MN-NM)^(T) = (MN)^(T)- (NM)^(T) =N^(T) M^(T) - M^(T)N^(T) ` `= NM=MN ` [`because`+ M, N are symmetric] `=-(MN-NM)` `therefore ` correct (c) `(MN)^(T) = N^(T) M^(T) = NMneMN` [`because` M, N are symmetric] `therefore` Incorrect. (d) `(adj M) (adjN) = adj (NM) ne adj(MN)` `therefore ` Incorrect. |
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