Manipal Engineering Manipal Engineering Solved Paper-2008

  • question_answer
    If\[A=[{{a}_{ij}}]\]is a4\[4\times 4\]matrix\[{{C}_{ij}}\]is the cofactor of the element\[{{a}_{ij}}\]in\[\left| A \right|\], then the expression\[{{a}_{11}}{{C}_{11}}+{{a}_{12}}{{C}_{12}}+{{a}_{13}}{{C}_{13}}+{{a}_{14}}{{C}_{14}}\]equal to

    A)  0                            

    B)         -1

    C)  1                            

    D)        \[\left| A \right|\]

    Correct Answer: D

    Solution :

    By definition. Any row of a matrix/ determinant\[A\]when multiplied by its corresponding cofactors results in the value of\[|A|\].


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