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Math / Linear Algebra 4 / Chapter 5.1 / Problem 3

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

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For each of the following matrices A G MnXn (F), (i) Determine all the eigenvalues of A

Chapter 5, Problem 3

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QUESTION:

For each of the following matrices A G MnXn (F), (i) Determine all the eigenvalues of A. (ii) For each eigenvalue A of A, find the set of eigenvectors corresponding to A. If possible, find a basis for Fn consisting of eigenvectors of A. If successful in finding such a basis, determine an invertible matrix Q and a diagonal matrix D such that Q~x AQ = D. = R for F = R (hi; (iv; for F = C for F = R

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QUESTION:

For each of the following matrices A G MnXn (F), (i) Determine all the eigenvalues of A. (ii) For each eigenvalue A of A, find the set of eigenvectors corresponding to A. If possible, find a basis for Fn consisting of eigenvectors of A. If successful in finding such a basis, determine an invertible matrix Q and a diagonal matrix D such that Q~x AQ = D. = R for F = R (hi; (iv; for F = C for F = R

ANSWER:

Step 1 of 16

Part (a)

Consider the matrix

(i)

Determine the eigenvalues of the matrix A.

Solve further as,

Now,

Hence the eigenvalues of the matrix A are 4 and -1.

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