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eigenvalues and eigenvectors for 2×2 and 3×3 matrices with full working
[
matrix size
]
(•)
2×2
( )
3×3
[
matrix (space-separated rows, one row per line)
]
4 1 2 3
[
eigenvalues
]
λ1
5
λ2
2
[
eigenvectors (normalized)
]
v1
[0.707107, 0.707107]
v2
[0.447214, -0.894427]
[
working
]
Characteristic polynomial: λ² - 7λ + 10 = 0
Discriminant: Δ = tr² - 4·det = 7² - 4·10 = 9
λ₁ = (7 + √9) / 2 = 5
λ₂ = (7 - √9) / 2 = 2
v₁ = [1, 1] → normalized [0.707107, 0.707107]
v₂ = [1, -2] → normalized [0.447214, -0.894427]
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