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

The system of linear equations
λx+2y+2z=5
2λx+3y+5z=8
4x+λy+6z=10 has
  1. no solution when λ=8
  2. a unique solution when λ=-8
  3. no solution when λ=2
  4. infinitely many solutions when λ=2

Solution

=λ222λ354λ6=λ18-5λ-212λ-20+22λ2-12=-λ2-6λ+16=λ+82-λ
=0 for λ=2,
1=5228351026

1=518-10-248-50+216-30

1=40+4-280
No solution for λ=2.

Asked in: JEE Main 2020 (08 Jan Shift 2)

Practice more Determinants questions on Aicharya