2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Determinants & Matrices

JEE Main & Advanced Mathematics Determinants & Matrices Question Bank System of linear equations, Some special determinants, differentiation and integration of determinants

  • question_answer
    The system of equations \[{{x}_{1}}-{{x}_{2}}+{{x}_{3}}=2,\] \[\,3{{x}_{1}}-{{x}_{2}}+2{{x}_{3}}=-6\]and  \[3{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=-18\] has [AMU 2001]

    A) No solution

    B) Exactly one solution

    C) Infinite solutions

    D) None of these

    Correct Answer: C

    Solution :

            \[D=\left| \,\begin{matrix}    1 & -1 & 1  \\    3 & -1 & 2  \\    3 & 1 & 1  \\ \end{matrix}\, \right|\,=\,1[-1-2]-1[6-3]+1[3+3]=0\] and\[{{D}_{1}}=\left| \,\begin{matrix}    2 & -1 & 1  \\    -6 & -1 & 2  \\    -18 & 1 & 1  \\ \end{matrix}\, \right|\,=2(-1-2)-1(-36+6)+1(-6-18)\]                \[=-6+30-24=0\] Also, \[{{D}_{2}}=0;\,{{D}_{3}}=0\] So the system is consistent \[(D={{D}_{1}}={{D}_{2}}={{D}_{3}}=0)\] i.e. system has infinite solution.


You need to login to perform this action.
You will be redirected in 3 sec spinner