JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Expansion of determinants, Solution of equation in the form of determinants and properties of determinants

  • question_answer
    \[\left| \,\begin{matrix}    x & 4 & y+z  \\    y & 4 & z+x  \\    z & 4 & x+y  \\ \end{matrix}\, \right|=\] [Karnataka CET 1991]

    A) 4

    B) \[x+y+z\]

    C) xyz

    D) 0

    Correct Answer: D

    Solution :

    Apply \[{{C}_{1}}\to {{C}_{1}}+{{C}_{3}}\] and take \[x+y+z\] common from \[{{C}_{1}}\] and 4 from \[{{C}_{2}}\] to make first two columns identical.


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