A-LevelFurther MathematicsMatrices and EigenvaluesOct/Nov 2011Paper 1 Q811 Marks
The vector e is an eigenvector of the matrix A, with corresponding eigenvalue λ, and is also an eigenvector of the matrix B, with corresponding eigenvalue μ. Show that e is an eigenvector of the matrix AB with corresponding eigenvalue λμ. [2] State the eigenvalues of the matrix C, where C = ( -1 -1 3 ) ( 0 1 2 ) ( 0 0 2 ) and find corresponding eigenvectors. [4] Show that `(1 6 3)ᵀ` is an eigenvector of the matrix D, where D = ( 1 -1 1 ) ( -6 -3 4 ) ( -9 -3 7 ) and state the corresponding eigenvalue. [3] Hence state an eigenvector of the matrix CD and give the corresponding eigenvalue. [2]
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