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J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    The system of equations \[2x-y+z=0,\]\[ax-y+2z=0\]and \[x-2y+z=0\] has non-zero solution, if a is equal to

    A)  \[1\]     

    B)  \[2\]    

    C) \[4\]  

    D)  \[5\]         

    Correct Answer: D

    Solution :

    Given, system of linear homogeneous equation, \[2x-y+z=0\] \[ax-y+2z=0\] \[x-2y+z=0\] If the system have non-zero solution, then \[D=0\] \[\left| \begin{matrix}    2 & -1 & 1  \\    a & -1 & 2  \\    1 & -2 & 1  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(-1+4)+(a-2)+(-2a+1)=0\] \[\Rightarrow \] \[6+a-2-2a+1=0\] \[\Rightarrow \] \[-a+5=0\,\,\Rightarrow a=5\]


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