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Determine the number of real values of lambda for which the system 2x - 3y + 5z = 9 x + 3y - z = -18 3x - y + (lambda² - |lambda|)z = 16 has no solution.
- 0
- 1
- 2
- 4
Correct answer: 2
Solution
Expanding the coefficient determinant gives D = 9k - 43 with k = lambda² - |lambda|; D = 0 at k = 43/9, and solving lambda² - |lambda| = 43/9 gives |lambda| = (1 + sqrt(181)/3)/2, so two real values lambda = +/-(that magnitude) make the system inconsistent.
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