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
    Let \[\left| \,\begin{matrix}    6i & -3i & 1  \\    4 & 3i & -1  \\    20 & 3 & i  \\ \end{matrix}\, \right|=x+iy\], then [IIT 1998]

    A) \[x=3,y=1\]

    B) \[x=0,y=0\]

    C) \[x=0,y=3\]

    D) \[x=1,y=3\]

    Correct Answer: B

    Solution :

    \[{{(a+b+c)}^{2}}\,\left| \,\begin{matrix}    2bc & -2c & -2b  \\    {{b}^{2}} & c+a-b & 0  \\    {{c}^{2}} & 0 & a+b-c  \\ \end{matrix}\, \right|\] \[\Rightarrow \] \[6i(-3+3)+3i(4i+20)+1(12-60i)=x+iy\] \[\Rightarrow \] \[({{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}})\] \[\Rightarrow \]  \[x=0,\,y=0\].


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