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JEE Main201815 Apr 2018Morning ShiftMathematicsDeterminantsActual

Let S be the set of all real values of k for which the system of linear equations aligned &x+y+z=2 &2 x+y-z=3 &3 x+2 y+k z=4 aligned has a unique solution. Then S is

Options

  1. Aan empty set
  2. Bequal to R - 0
  3. Cequal to 0
  4. Dequal to R

Correct answer

B. equal to R - 0

Step-by-step solution

The system of linear equations is: aligned &x+y+z=2 &2 x+y-z=3 &3 x+2 y+k z=4 aligned As, system has unique solution. aligned & So, | array ccc 1 & 1 & 1 2 & 1 & -1 3 & 2 & k array | 0 & k+2-(2 k+3)+1 0 & k 0 aligned Hence, k R- 0 S

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