T:R² → R²
T(x, y) = (y, x); (x, y)∈R²

Eigenvalues

• Eigenvalues of T are --Select-- 2 & 1 1 & -1 1 & 0 1 & 1 Submit

Eigenvectors

• Corresponding to eigenvalue 1

• --Select-- (2, 1) (1, 1) (1, 2) (-1, 1) is an eigenvector Submit

• In general, an eigenvector is --Select-- (-𝑥, 𝑥), 𝑥 ≠ 0, 𝑥 ∈ 𝑅 (𝑥, -𝑥), 𝑥 = 0, -𝑥 ∈ 𝑅 (𝑥, 𝑥), 𝑥 ≠ 0, 𝑥 ∈ 𝑅 (𝑥, -𝑥), 𝑥 ≠ 0, 𝑥 ∈ 𝑅 Submit

• Corresponding to eigenvalue -1

• --Select-- (1, -1) (1, 1) (-1, -1) (-1, 2) is an eigenvector. Submit

• In general, an eigenvector is --Select-- (-𝑥, 𝑥), 𝑥 ≠ 0, 𝑥 ∈ 𝑅 (𝑥, -𝑥), 𝑥 ∈ 𝑅 (𝑥, 𝑥), 𝑥 ≠ 0, 𝑥 ∈ 𝑅 (𝑥, 𝑥), 𝑥 = 0, 𝑥 ∈ 𝑅 Submit

Visualization

Excersise: Draw a diagram showing images of (1, 1), (1, 2) and (-1, 1) to determine which of these are eigenvectors, by visualization.
Answer: Click here