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Math / Linear Algebra: A Geometric Approach 2 / Chapter 6.1 / Problem 6

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

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Suppose A is nonsingular. Prove that the eigenvalues of A 1 are the reciprocals of the

Chapter 6, Problem 6

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QUESTION:

Suppose A is nonsingular. Prove that the eigenvalues of A 1 are the reciprocals of the eigenvalues of A.

Questions & Answers

QUESTION:

Suppose A is nonsingular. Prove that the eigenvalues of A 1 are the reciprocals of the eigenvalues of A.

ANSWER:

Problem 6

Suppose A is non-singular. Prove that the eigenvalues of are the reciprocals of the eigenvalues of

Step by Step Solution

Step 1 of 2

According to the definition of eigenvalues of a matrix, if is an eigenvalues of , then satisfies the equation

(i)

Given that is non – singular. Therefore and exists.

To prove that the eigenvalues of are the reciprocals of the eigenvalues of.

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