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justification for your response. a. The eigenvalues of a matrix A are the entries on the diagonal of A. b. If A is an eigenvalue of multiplicity 1, then Ex is one-dimensional. c. If a matrix A is invertible, then A 0 cannot be an eigenvalue. - d. If A is a 13 x 13 matrix, the charasteristic polynomial has degree less than 13. e. The eigenspace Ex of A is the same as the null space Nul(A - XI).

justification for your response. a. The eigenvalues of a matrix A are the entries on the diagonal of A. b. If A is an eigenvalue of multiplicity 1, then Ex is one-dimensional. c. If a matrix A is invertible, then A 0 cannot be an eigenvalue. - d. If A is a 13 x 13 matrix, the charasteristic polynomial has degree less than 13. e. The eigenspace Ex of A is the same as the null space Nul(A - XI).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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e's 3. Determine whether the following statements are true or false and provide a justification for your response. a. The eigenvalues of a matrix A are the entries on the diagonal of A. b. If A is an eigenvalue of multiplicity 1, then Ex is one-dimensional. 0 cannot be an eigenvalue. c. If a matrix A is invertible, then A - d. If A is a 13 x 13 matrix, the charasteristic polynomial has degree less than 13. e. The eigenspace Ex of A is the same as the null space Nul(A - XI).
Transcribed Image Text:e's 3. Determine whether the following statements are true or false and provide a justification for your response. a. The eigenvalues of a matrix A are the entries on the diagonal of A. b. If A is an eigenvalue of multiplicity 1, then Ex is one-dimensional. 0 cannot be an eigenvalue. c. If a matrix A is invertible, then A - d. If A is a 13 x 13 matrix, the charasteristic polynomial has degree less than 13. e. The eigenspace Ex of A is the same as the null space Nul(A - XI).
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