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JEE Main & Advanced Sample Paper JEE Main Sample Paper-14

  • question_answer
    For the system of linear equation \[kx+y+z=1,\] \[x+ky+z=k\] and \[x+y+kz={{k}^{2}}\]. If \[k=1,\] then equation has

    A)  unique solution                            

    B)  infinitely many solutions

    C)  no solution                               

    D)  trivial solution

    Correct Answer: B

    Solution :

     If                            \[k=1,\] Then, \[D={{D}_{1}}={{D}_{2}}={{D}_{3}}=\,\left| \begin{matrix}    1 & 1 & 1  \\    1 & 1 & 1  \\    1 & 1 & 1  \\ \end{matrix} \right|=0\] Clearly, for k = 1 \[D={{D}_{1}}={{D}_{2}}={{D}_{3}}=0\] has infinitly many solutios.


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