The larger of the two eigenvalues of the matrix [[4, 5],[2, 1]] is _______
GATE 2015 · Engineering Mathematics · Eigen Value · easy
Answer: The larger of the two eigenvalues is 6.
- Write and solve the characteristic equation: Trace = 4 + 1 = 5. Det = (4)(1) - (5)(2) = 4 - 10 = -6. Characteristic equation: lambda^2 - 5*lambda - 6 = 0.
- Factor the quadratic to find eigenvalues: (lambda - 6)(lambda + 1) = 0 => lambda = 6 or lambda = -1. The larger eigenvalue is 6.