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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    The system of equations \[x+3y+2z=0\] \[3x+y+z=0\] and \[2x-2y-z=0\]

    A)  possesses a trivial solution only

    B)  possesses a non-zero unique solution

    C)  does not have a common non-zero solution

    D)  has infinitely many solutions

    Correct Answer: D

    Solution :

    Given system of equations are \[x+3y+2z=0\] \[3x+y+z=0\] and \[2x-2y-z=0\] Now, \[\Delta =\left| \begin{matrix}    1 & 3 & 2  \\    3 & 1 & 1  \\    2 & -2 & -1  \\ \end{matrix} \right|\] \[=1(-1+2)-3(-3-2)+2(-6-2)\] \[=1+15-16\] \[=0\] Since, determinant is zero, then it has infinitely many solutions.                           .


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