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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Self Evaluation Test - Matrices

  • question_answer
    If C is skew-symmetric matrix of order n and X is \[n\times 1\] column matrix, then X'CX is a

    A) Scalar matrix

    B) Unit matrix

    C) Null matrix

    D) None of these

    Correct Answer: C

    Solution :

    [c] Here, X is \[n\times 1,\] C is \[n\times n\] and \[X'\]is \[1\times n\] Hence, \[X'CX\] is \[1\times 1\] matrix. Let \[X'CX=k\]. Thus, \[(X'CX)'=X'C'X'=X'C'X'=X'(-C)X\] \[=-X'CX=-k\] \[\Rightarrow k=-k\Rightarrow k=0\Rightarrow X'CX\] is null matrix.


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