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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    Let \[A=\left( \begin{matrix}    {{x}^{2}} & 6 & 8  \\    3 & {{y}^{2}} & 9  \\    4 & 5 & {{z}^{2}}  \\ \end{matrix} \right),\]  \[B=\left( \begin{matrix}    2x & 3 & 5  \\    2 & 2y & 6  \\    1 & 4 & 2z-3  \\ \end{matrix} \right)\]  be two matrices and if Tr.  = Tr. , then the value of  \[(x+y+z)\] is equal to

    A)  0                                            

    B)  1

    C)  2                                            

    D)  3 [Note: Tr. (P) denotes trace of matrix P.J

    Correct Answer: D

    Solution :

    \[tr(A)={{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] \[tr(B)=2x+2y+2z-3\] \[{{(x-1)}^{2}}+{{(y-1)}^{2}}+{{(z-1)}^{2}}=0\] \[\therefore \]\[x=y=z=1\]Hence,\[(x+y+z)=3\].


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