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JEE Main & Advanced AIEEE Solved Paper-2010

  • question_answer
    Consider the system of linear equations : \[{{x}_{1}}+2{{x}_{2}}+{{x}_{3}}=3\] \[2{{x}_{1}}+3{{x}_{2}}+{{x}_{3}}=3\] \[3{{x}_{1}}+5{{x}_{2}}+2{{x}_{3}}=1\] The system has       AIEEE  Solved  Paper-2010

    A) Infinite number of solutions

    B) Exactly 3 solutions

    C) a unique solution

    D) No solution

    Correct Answer: D

    Solution :

    \[\Delta =\left| \begin{matrix}    1 & 2 & 1  \\    2 & 3 & 1  \\    3 & 5 & 2  \\ \end{matrix} \right|=1(1)-2(1)+1(1)=0\] \[{{\Delta }_{1}}=\left| \begin{matrix}    3 & 2 & 1  \\    3 & 3 & 1  \\    1 & 5 & 2  \\ \end{matrix} \right|=3(1)-2(5)+1(12)=5\] \[{{\Delta }_{1}}\ne 0\] When\[\Delta =0\]and if\[{{\Delta }_{1}},{{\Delta }_{2}},{{\Delta }_{3}},\]are not zero then no solution


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