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The values of λ and μ for which the equations x + y + z = 3, x + 3y + 2z = 6 and x + λy + 3z = μ have
  • a)
    A unique solution, if λ = 5, μ ∈ R
  • b)
    No solution, if  λ ≠ 5, μ =9
  • c)
    Infinite many solutions, if   λ = 5, μ ≠9
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The values of λ and μ for which the equations x + y + z = 3,...
Given x + y + z = 3, x + 3y + 2z = 6 and x + λy + 3z = μ
If Δ ≠  0 i.e. λ ≠ 0 the solution is unique.
Case 1 If λ ≠ 5 and μ s any real number, then unique solution exists 
Case 2 If  λ ≠ 5 ⇒ Δ = 0
If Δ≠ 0 , μ ≠ 9  the system has no solution.
Case 3 If λ = 5 and μ = 9, infinite solutions exist
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The values of λ and μ for which the equations x + y + z = 3,...
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The values of λ and μ for which the equations x + y + z = 3, x + 3y + 2z = 6 and x + λy + 3z = μhavea)A unique solution, if λ = 5, μ ∈ Rb)No solution, ifλ ≠ 5, μ =9c)Infinite many solutions, ifλ = 5, μ ≠9d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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