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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If\[\left[ \begin{matrix}    1 & -1 & x  \\    1 & x & 1  \\    x & -1 & 1  \\ \end{matrix} \right]\]has no inverse, then the real value of x is

    A)  2                            

    B)         3

    C)  0                            

    D)         1

    Correct Answer: D

    Solution :

    If matrix has no inverse it means the value of determinant should be zero. \[\therefore \]  \[\left| \begin{matrix}    1 & -1 & x  \\    1 & x & 1  \\    x & -1 & 1  \\ \end{matrix} \right|=0\] If we put\[x=1\], then column 1st and \[IIIrd\] are identical. Hence, option (d) is correct.


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