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Given a Matrix A and B and we know that V is an eigenvector of A and

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Given a Matrix A and B and we know that V is an
eigenvector of A and B with eigenvalues Y and Z: a: Is V
an eigenvector of AB and if so which eigenvalue? b: Is V
an eigenvector of A+B and if so which eigenvalue?
Solution
Simply apply the matrix to the eigenvector
and the result falls out Bv = Zv Thus, ABv = AZv = ZAv =
ZYv, so ABv = ZYv, and v is the eigenvector with
eigenvalue ZY or YZ Similarly, (A+B)v = Av +Bv = Yv +Zv
= (Y+Z)v, so v is an eigenvector with eigenvalue Y+Z

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Given a Matrix A and B and we know that V is an eigenvector of A and B with eigenvalues Y and Z: a: Is V an eigenvector of AB and if so which eigenvalue? b: Is V an eigenvector of A+B and if so which eigenvalue? Solution Simply apply the matrix to the eigenvector and the result falls out Bv = Zv T ...
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