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JEE Main 201815 AprilMorning ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Morning Shift
Mode
Online
Subject
Mathematics
Chapter
Determinants

JEE Main 2018 · 15 April · Morning Shift · Online · Mathematics · Determinants

Let S be the set of all real values of k for which the system of...

Let SS be the set of all real values of kfork forwhich the system of linear equations x+y+z=22x+y−z=33x+2y+kz=4\begin{aligned} &x+y+z=2 \\ &2 x+y-z=3 \\ &3 x+2 y+k z=4 \end{aligned} has a unique solution. ThenSS is

Options

  1. Aan empty set
  2. Bequal to R−{0}\mathrm{R}-\{0\}
  3. Cequal to {0}\{0\}
  4. Dequal to R\mathrm{R}

Correct answer

B. equal to R−{0}\mathrm{R}-\{0\}

Step-by-step solution

The system of linear equations is: \begin{aligned} &x+y+z=2 \\ &2 x+y-z=3 \\ &3 x+2 y+k z=4 \end{aligned} As, system has unique solution. \begin{aligned} &\text{ So, }\left|\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k \end{array}\right| \neq 0 \\ &\Rightarrow k+2-(2 k+3)+1 \neq 0 \\ &\Rightarrow k \neq 0 \end{aligned}$$Hence,Hence,k \in R-\{0\} \equiv S$
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