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

  • question_answer
    If \[{{A}_{1}},{{A}_{3}},.......,{{A}_{2n-1}}\] are n skew-symmetric matrices of same order, then \[B=\sum\limits_{r=1}^{n}{(2r-1){{({{A}_{2r-1}})}^{2r-1}}}\] will be

    A) Symmetric

    B) Skew-symmetric

    C) Neither symmetric nor skew-symmetric

    D) Data is adequate

    Correct Answer: B

    Solution :

    [b] \[B={{A}_{1}}+3A_{3}^{3}+.....(2n-1){{({{A}_{2n-1}})}^{2n-1}}\] \[{{B}^{T}}=-[{{A}_{1}}+3A_{3}^{3}+....(2n-1){{({{A}_{2r-1}})}^{2r-1}}]\]             \[=-B\], so skew-symmetric


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