If the system of equations x + y + z = 2 2   x + 4   y - z = 6 3 x + 2 y + λ z = μ has…

If the system of equations

x+y+z=2
2 x+4 y-z=6
3x+2y+λz=μ

has infinitely many solutions, then :

  1.  λ+2μ=14
  2. 2λ-μ=5
  3. λ-2μ=-5
  4. 2λ+μ=14

Solution

For infinitely many solutions, all determinants should be zero.

D=11124-132λ=0⇒λ=92

D3=11224632μ=0⇒μ=5

Now check each option 

Asked in: JEE Main 2020 (04 Sep Shift 2)

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