For the system of linear equations: x - 2 y = 1 , x - y + k z = - 2 , k y + 4 z = 6 , k ∈ R Consider the following statements: (A) The system has unique solution if k ≠ 2 , k ≠ - 2 . (B) The system ha

Question

For the system of linear equations: x - 2 y = 1 , x - y + k z = - 2 , k y + 4 z = 6 , k ∈ R Consider the following statements: (A) The system has unique solution if k ≠ 2 , k ≠ - 2 . (B) The system has unique solution if k = - 2 . (C) The system has unique solution if k = 2 . (D) The system has no-solution if k = 2 . (E) The system has infinite number of solutions if k ≠ - 2 . Which of the following statements are correct?

TestHub · Accepted Answer

D = 1 - 2 0 1 - 1 k 0 k 4 = 4 - k 2 so, A is correct and B , C , E are incorrect. If k = ± 2 D 1 = 1 - 2 0 - 2 - 1 2 6 2 4 = - 48 ≠ 0 So, no solution if k = ± 2

Mathematics - Determinant Question with Solution | TestHub

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