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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    The system\[x+4y-2z=3,\,\]\[3x+y+5z=7,\] \[2x+3y+z=5\]has:

    A)  infinite number of solutions

    B)         unique solution

    C)         trivial solution

    D)         no solution

    E)         multiple solutions

    Correct Answer: D

    Solution :

    Given system of equations are \[x+4y-2z=3\] \[3x+y+5z=7\] \[2x+3y+z=5\] \[\therefore \]  \[\Delta =\left| \begin{matrix}    1 & 4 & -2  \\    3 & 1 & 5  \\    2 & 3 & 1  \\ \end{matrix} \right|\]                 \[=1(1-15)-4(3-10)-2(9-2)\]                 \[=-14+28-14=0\] Since,\[\Delta =0\]and\[{{\Delta }_{2}}\ne 0\] \[\therefore \]  No solution will exist.


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