The system of equations - k x + 3 y - 14 z = 25 - 15 x + 4 y - k z = 3 - 4 x + y + 3 z = 4 Question: is…

The system of equations
-kx+3y-14z=25

-15x+4y-kz=3

-4x+y+3z=4

Question: is consistent for all k in the set

  1. R
  2. R--11,13
  3. R--13
  4. R--11,11

Solution

For consistent solutions ∆≠0

⇒-k3-14-154-k-413≠0

⇒  -k12+k-3-45-4k-14-15+16≠0

⇒ -12k-k2+135+12k-14≠0

⇒ k2≠121

⇒ k≠11,-11

Asked in: JEE Main 2022 (25 Jun Shift 2)

Practice more Determinants questions on Aicharya