Find the singular value decomposition of A = 22 -1 1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.3: The Inverse Of A Matrix
Problem 80E
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Question
4.9
![**Exercise 4.9: Singular Value Decomposition**
**Objective:**
Find the singular value decomposition of the matrix \( A \).
**Matrix \( A \):**
\[
A = \begin{bmatrix} 2 & 2 \\ -1 & 1 \end{bmatrix}
\]
**Instructions:**
Use appropriate methods to calculate the singular value decomposition, ensuring to determine the matrices \( U \), \( \Sigma \), and \( V^T \) such that \( A = U \Sigma V^T \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e25041d-7573-46df-b9d3-ec2dd7694c16%2Fcf716113-d236-477a-9cab-8e53c35efaf9%2Fccvsexn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise 4.9: Singular Value Decomposition**
**Objective:**
Find the singular value decomposition of the matrix \( A \).
**Matrix \( A \):**
\[
A = \begin{bmatrix} 2 & 2 \\ -1 & 1 \end{bmatrix}
\]
**Instructions:**
Use appropriate methods to calculate the singular value decomposition, ensuring to determine the matrices \( U \), \( \Sigma \), and \( V^T \) such that \( A = U \Sigma V^T \).
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Step 1: Definition of singular value decomposition of a matrix
VIEWStep 2: Determine the eigenvalues of A^TA
VIEWStep 3: Determine the corresponding eigenvectors
VIEWStep 4: Determine the matrix V^T and the singular values of A
VIEWStep 5: Determine the eigenvalues and eigenvectors of AA^T
VIEWStep 6: Determine the matrix U and singular value decomposition of A
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