The matrix P has eigenvector e with corresponding eigenvalue 2, and the matrix Q also has eigenvector

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The matrix P has eigenvector e with corresponding eigenvalue 2, and the matrix Q also has eigenvector e with corresponding eigenvalue µ.

Find the corresponding eigenvalues and eigenvectors for the matrices P + Q and PQ.

The matrix A is given as


b. State the eigenvalues, and find the eigenvectors of the matrix A.

The matrix B = A + 21.

c. Find the eigenvalues and eigenvectors of the matrices A + B and AB.  

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