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

The following system of linear equations
7x+6y-2z=0
3x+4y+2z=0
x-2y-6z=0, has
  1. infinitely many solutions, x,y,z satisfying y=2z
  2. no solution
  3. infinitely many solutions, x,y,z satisfying x=2z
  4. only the trivial solution

Solution

76-23421-2-6

=7-20-6-20-2-10

=-140+120+20=0

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

Asked in: JEE Main 2020 (09 Jan Shift 2)

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