A-LevelFurther MathematicsEigenvalues and EigenvectorsMay/June 2013Paper 1 Q69 Marks
The matrix A is given by A = [[4, -5, 3], [3, -4, 3], [1, -1, 2]] Show that e = [[1], [1], [1]] is an eigenvector of A and state the corresponding eigenvalue. Find the other two eigenvalues of A. The matrix B is given by B = [[-1, 4, 0], [-1, 3, 1], [1, -1, 3]] Show that e is an eigenvector of B and deduce an eigenvector of the matrix AB, stating the corresponding eigenvalue.
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