Verified Solution • 2025–26 Session moderate

QJEEM20Ma9399: JEE Main 2020 Mathematics - Class 12 JEEM20Ma9399 Solution: The system of linear equations x + 2y + 2z = 5 2 x + 3y + 5z =…

The system of linear equations
λ\lambda x + 2y + 2z = 5
2 λ\lambda x + 3y + 5z = 8
4x + λ\lambda y + 6z = 10 has

Multiple Choice Options

  • A a unique solution when λ\lambda = –8
  • B no solution when λ\lambda = 2
  • C infinitely many solutions when λ\lambda = 2
  • D no solution when λ\lambda = 8

Step-by-Step Verified Solution

Δ\Delta = |λ222λ354λ6|

= λ\lambda ( 18 – 5 λ\lambda ) – 2(12 λ\lambda – 20) + 2(2 λ\lambda 2 – 12)

= 18 λ\lambda – 5 λ\lambda 2 – 24 λ\lambda + 40 + 4 λ\lambda 2 – 24

= – λ\lambda 2 – 6 λ\lambda + 16

= – ( λ\lambda + 8)( λ\lambda – 2)

For no solutions λ\lambda = 0 ⇒\Rightarrow λ\lambda = – 8, λ\lambda = 2

when λ\lambda = 2

Δ\Delta x = |5228351026|

= 5 (18 – 10) – 2 (48 – 50) + 2 (16 – 30)

= 40 + 4 – 28 ≠\ne 0

So no solution for λ\lambda = 2

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