4. Diagonalization Prove that a square matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. • Determine whether the following matrix is diagonalizable: [54 2 B = 01 -1 3
4. Diagonalization Prove that a square matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. • Determine whether the following matrix is diagonalizable: [54 2 B = 01 -1 3
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 66CR
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Question
![4. Diagonalization
Prove that a square matrix A is diagonalizable if and only if A has n linearly independent
eigenvectors.
•
Determine whether the following matrix is diagonalizable:
[54
2
B =
01
-1
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6527c97f-bcd7-44bb-a52a-9c5764f88724%2Fb76bf529-096a-41dc-be2f-cf3751a24179%2Fy280pco_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Diagonalization
Prove that a square matrix A is diagonalizable if and only if A has n linearly independent
eigenvectors.
•
Determine whether the following matrix is diagonalizable:
[54
2
B =
01
-1
3
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