What are the eigenvalues of the matrix A = [[4, 1], [2, 3]]?
Answer and explanation
Correct answer: A. lambda = 5 and lambda = 2
- Step 1: Characteristic equation: det(A - lambdaI) = 0 => (4 - lambda)(3 - lambda) - 2 = 0. Step 2. lambda^2 - 7lambda + 12 - 2 = 0 => lambda^2 - 7lambda + 10 = 0 => (lambda - 5)(lambda - 2) = 0. Answer: lambda = 5 and lambda = 2. Why not the others:* The eigenvalues are lambda = 5 and lambda = 2.
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