Mathematics · Matrices
Consider a 2 × 2 matrix A = 0111 which has eigenvalues λ1 = 1 + √52 and λ2 = 1 - √52. For any natural number n, which of the following is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1An = 1√5 λ1n-1 - λ2n-1λ1n - λ2nλ1n - λ2nλ1n+1 - λ2n+1✓
- 2An = 1√5 λ1n-1 - λ2n-1λ1n - λ2nλ1n+1 - λ2n+1λ1n+1 - λ2n+1
- 3An = 1√5 λ1n-1 + λ2n-1λ1n + λ2nλ1n+1 + λ2n+1λ1n+1 + λ2n+1
- 4An = 1√5 λ1n-1 + λ2n-1λ1n - λ2nλ1n + λ2nλ1n+1 - λ2n+1
Correct answer
An = 1√5 λ1n-1 - λ2n-1λ1n - λ2nλ1n - λ2nλ1n+1 - λ2n+1
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