A-LevelFurther MathematicsEigenvalues and EigenvectorsMay/June 2014Paper 1 Q910 Marks
The matrix M, where M = [ [-2, 2, 2], [2, 1, 2], [-3, -6, -7] ], has an eigenvector (0, 1, -1)^T. Find the corresponding eigenvalue. It is given that if the eigenvalues of a general 3 × 3 matrix A, where A = [ [a, b, c], [d, e, f], [g, h, i] ], are λ₁, λ₂ and λ₃ then λ₁ + λ₂ + λ₃ = a + e + i and the determinant of A has the value λ₁λ₂λ₃. Use these results to find the other two eigenvalues of the matrix M, and find corresponding eigenvectors.
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