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JEE Main 20127 MayOnline
Exam
JEE Main
Year
2012
Date
7 May
Mode
Online
Subject
Mathematics
Chapter
Determinants

JEE Main 2012 · 7 May · Online · Mathematics · Determinants

If the system of equations aligned & x+y+z=6 & x+2 y+3 z=10 & x+2...

If the system of equations x+y+z=6x+2y+3z=10x+2y+λz=0\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 λ\lambda is not equal to

Options

  1. A1
  2. B0
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

Given system of equations is x+y+z=6x+2y+3z=10x+2y+λz=0\begin{aligned}& x+y+z=6 \\ & x+2 y+3 z=10 \\ & x+2 y+\lambda z=0 \end{aligned}It has unique solution. ∴∣11112312λ∣≠0⇒1(2λ−6)−1(λ−3)+1(2−2)≠0⇒2λ−6−λ+3≠0⇒λ−3≠0⇒λ≠3\begin{aligned}& \therefore \left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 2 & \lambda \end{array}\right| ≠ 0 \\ & \Rightarrow \quad 1(2 \lambda-6)-1(\lambda-3)+1(2-2) ≠ 0 \\ & \Rightarrow \quad 2 \lambda-6-\lambda+3 ≠ 0 \Rightarrow \lambda-3 ≠ 0 \Rightarrow \lambda ≠ 3 \end{aligned}
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