Q39 / 90 · JEE Main 2012 (07 May Online) · Mathematics

If the system of equations $$ \begin{aligned} & x+y+z=6 \\ & x+2 y+3 z=10 \\ & x+2 y+\lambda z=0 \end{aligned} $$ has a unique solution, then $\lambda$ is not equal to

  • A
    1
  • B
    0
  • C
    2
  • Correct answer
    D
    3

Solution

Given system of equations is $$ \begin{aligned} & x+y+z=6 \\ & x+2 y+3 z=10 \\ & x+2 y+\lambda z=0 \end{aligned} $$ It has unique solution. $$ \begin{aligned} & \therefore\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 2 & \lambda \end{array}\right| \neq 0 \\ & \Rightarrow \quad 1(2 \lambda-6)-1(\lambda-3)+1(2-2) \neq 0 \\ & \Rightarrow \quad 2 \lambda-6-\lambda+3 \neq 0 \Rightarrow \lambda-3 \neq 0 \Rightarrow \lambda \neq 3 \end{aligned} $$

Hence, the correct answer is option: 'D'.

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