Mathematics · Linear Algebra
Let A be a 3 × 3 matrix with a single eigenvalue λ that has algebraic multiplicity 3. Which of the following statements is true about A?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1A has three distinct linearly independent eigenvectors.
- 2A is not diagonalizable.
- 3A is always diagonalizable.
- 4A is diagonalizable if and only if the geometric multiplicity of λ is 3.✓
Correct answer
A is diagonalizable if and only if the geometric multiplicity of λ is 3.
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