Linear AlgebraShow full work neatly and box final answer.Thanks 13Consider the matrix A =3-21. 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-Schmidtorthonormalization 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 matrix P-l AP

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Answered: 1 3 Consider the matrix A = 3 1 -2 1.…

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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Linear Algebra

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1
3
Consider the matrix A =
3
-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 matrix P-l AP

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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