Mathematics · Linear Algebra
Suppose A is a 5 × 5 block diagonal real matrix with diagonal blocks given by: ⌈ e 1 ⌉ ⌊ 0 e ⌋ and ⌈ e 1 0 ⌉ ⌈ 0 e 0 ⌉ ⌊ 0 0 e ⌋. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The geometric multiplicity of e in A is 1.
- 2The geometric multiplicity of e in A is 3.
- 3A is diagonalizable over the real numbers.
- 4The algebraic multiplicity of e in A is 5.✓
Correct answer
The algebraic multiplicity of e in A is 5.
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