SHOW WORK! This is based on material in Section 7.3. 1 3 Consider the matrix A = |3 1 0 0 -2 1. Why is the matrix A orthogonally diagonalizable? 2. Find all the eigenvalues of A and determine the multiplicity of each. 3. For each eigenvalue of A of multiplicity 1, find an eigenvector of length 1. 4. For each eigenvalue of A of multiplicity k >1, find a set of k linearly independent eigenvectors. If this set of not orthonormal, apply Gram-Schmidt orthonormalization process to get an orthonormal set of eigenvectors. 5. Parts 3 and 4 give us an orthonormal set of n eigenvectors. Use these eigenvectors to form the matrix P. 6. Calculate the inverse of P. 7. Find the matrixP-'AP
SHOW WORK! This is based on material in Section 7.3. 1 3 Consider the matrix A = |3 1 0 0 -2 1. Why is the matrix A orthogonally diagonalizable? 2. Find all the eigenvalues of A and determine the multiplicity of each. 3. For each eigenvalue of A of multiplicity 1, find an eigenvector of length 1. 4. For each eigenvalue of A of multiplicity k >1, find a set of k linearly independent eigenvectors. If this set of not orthonormal, apply Gram-Schmidt orthonormalization process to get an orthonormal set of eigenvectors. 5. Parts 3 and 4 give us an orthonormal set of n eigenvectors. Use these eigenvectors to form the matrix P. 6. Calculate the inverse of P. 7. Find the matrixP-'AP
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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Transcribed Image Text:SHOW WORK! This is based on material in Section 7.3.
1 3
Consider the matrix A = |3 1
0 0 -2
1. Why is the matrix A orthogonally diagonalizable?
2. Find all the eigenvalues of A and determine the multiplicity of each.
3. For each eigenvalue of A of multiplicity 1, find an eigenvector of length 1.
4. For each eigenvalue of A of multiplicity k >1, find a set of k linearly independent eigenvectors. If this set of not
orthonormal, apply Gram-Schmidt orthonormalization process to get an orthonormal set of eigenvectors.
5. Parts 3 and 4 give us an orthonormal set of n eigenvectors. Use these eigenvectors to form the matrix P.
6. Calculate the inverse of P.
7. Find the matrixP-'AP
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