Suppose be a scalar different from the eigenvalues of A,

Chapter 5, Problem 15E

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QUESTION:

Problem 15E

Suppose  be a scalar different from the eigenvalues of A, and let  from both sides of the equation , and use algebra to show that  is an eigenvalue of B, with x a corresponding eigenvector.

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QUESTION:

Problem 15E

Suppose  be a scalar different from the eigenvalues of A, and let  from both sides of the equation , and use algebra to show that  is an eigenvalue of B, with x a corresponding eigenvector.

ANSWER:

Solution 15E

Consider that, with, andbe a scalar.

And, suppose that.

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