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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    The matrix \[\left| \begin{matrix}    5 & 10 & 3  \\    -2 & -4 & 6  \\    -1 & -2 & b  \\ \end{matrix} \right|\]is a singular matrix, if b is equal to:

    A)  \[-3\]                                   

    B)  3                            

    C)  0                            

    D)         for any value of b

    E)  for no value of b

    Correct Answer: D

    Solution :

    The matrix\[\left[ \begin{matrix}    5 & 10 & 3  \\    -2 & -4 & 6  \\    -1 & -2 & b  \\ \end{matrix} \right]\]is singular, if \[\left| \begin{matrix}    5 & 10 & 3  \\    -2 & -4 & 6  \\    -1 & -2 & b  \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[-1(60+12)+2(30+6)\]                                                 \[+b(-20+20)=0\] \[\Rightarrow \]               \[-72+72+0b=0\] The given matrix is singular for any value of b.


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