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QJEEM18Ma6f60: JEE Main 2018 Mathematics - Class 12 JEEM18Ma6f60 Solution: Let S be the set of all real values of k for which the systemof …

Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y − z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :

Multiple Choice Options

  • A an empty set
  • B equal to {0}
  • C equal to R
  • D equal to R − {0}

Step-by-Step Verified Solution

As system of linear equations have unique solutions so, determinant of coefficient ≠ 0

∴ |11121−132k| ≠ 0

⇒ k + 2 - (2k + 3) + 1 ≠ 0

⇒ k ≠ 0

∴ k ∈ R - {0}

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