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JEE Main20209 Jan 2020Evening ShiftMathematicsDeterminantsActual

The following system of linear equations 7 x + 6 y - 2 z = 0 3 x + 4 y + 2 z = 0 x - 2 y - 6 z = 0 , has

Options

  1. Ainfinitely many solutions, x , y , z satisfying y = 2 z
  2. Bno solution
  3. Cinfinitely many solutions, x , y , z satisfying x = 2 z
  4. Donly the trivial solution

Correct answer

C. infinitely many solutions, x , y , z satisfying x = 2 z

Step-by-step solution

7 6 - 2 3 4 2 1 - 2 - 6 = 7 - 20 - 6 - 20 - 2 - 10 = - 140 + 120 + 20 = 0 So infinite non-trivial solution exist Now equation ( 1 ) + 3 equation ( 3 ) ⇒ 10 x - 20 z = 0 ⇒ x = 2 z

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