Let S be the set of all real values of k for which the system of linear equations x + y + z = 2 2 x + y - z…

Let S be the set of all real values of k for which the system of linear equations
x+y+z=2
2x+y-z=3
3x+2y+kz=4
has a unique solution. Then, S is :
  1. equal to R –{0}
  2. an empty set
  3. equal to R
  4. equal to 0

Solution

For unique solution, ∆≠0

⇒11121-132k≠0

⇒1k+2-12k+3+14-3≠0

 ⇒-k≠0⇒k≠0

Thus, S=R-0

Asked in: JEE Main 2018 (15 Apr)

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