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JEE Main 201815 April
Exam
JEE Main
Year
2018
Date
15 April
Subject
Mathematics
Chapter
Determinants

JEE Main 2018 · 15 April · 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 kk for which the system of linear equations
x+y+z=2x + y + z = 2
2x+y−z=32x + y - z = 3
3x+2y+kz=43x + 2y + kz = 4
has a unique solution. Then, SSis :

Options

  1. Aequal to R–0R – { 0 }
  2. Ban empty set
  3. Cequal to RR
  4. Dequal to {0}\left\{0\right\}

Correct answer

A. equal to R–0R – { 0 }

Step-by-step solution

For unique solution, ∆≠0∆ \ne 0

⇒ \left|\begin{cases}1 & 1 & 1 \\ 2 & 1 & - 1 \\ 3 & 2 & k\end{cases}\right| \ne 0

⇒1(k+2)−1(2k+3)+1(4−3)≠0⇒ 1\left(k + 2\right) - 1\left(2k + 3\right) + 1\left(4 - 3\right) \ne 0

⇒−k≠0⇒k≠0⇒ - k \ne 0 ⇒ k \ne 0

Thus, S=R−{0}S = R - \left\{0\right\}

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