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The system of linear equations

3x -2y -kz = 10

2x -4y -2z = 6

x + 2y -z = 5m

is inconsistent if

 

Option 1 -

k ≠ 3 ,     m ≠ 4 5

Option 2 -

k = 3 ,     m ≠ 4 5

Option 3 -

k ≠ 3 ,     m ∈ R

Option 4 -

k = 3, m = 4 5

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago
    Correct Option - 1


    Detailed Solution:

      Δ − | 3 − 2 − k 2 − 4 − 2 1 2 − 1 | = | 3 − 2 − k 0 − 8 0 1 2 − 1 | , [ R 2 − R 1 − 2 R 3 ]

    = -8 (-3 + k)

    For inconsistent Δ = 0 ⇒ k = 3  

    Δ x = | 1 0 − 2 − k 6 − 4 − 2 5 m 2 − 1 | = 3 2 − 4 0 m ≠ 0 ⇒ m ≠ 4 5

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