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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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
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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