Mathematics · Linear Algebra
Let T : &complex;n → &complex;n be a linear transformation, n ≥ 2. Suppose 1 is the only eigenvalue of T. Which of the following statements is always true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(T - I)n+1 ≠ 0
- 2(T - I)n = 0✓
- 3(T - I)n-1 = 0
- 4Tk ≠ I for any k ∈ ℕ
Correct answer
(T - I)n = 0
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