Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Show that the matrix is not diagonalizable.

 
2 −4 2
 
0 2 3
0 0 3
STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.)
 
(?1, ?2) = 
 
 
 
 
 
   
STEP 2: Find the eigenvectors x1 and x2 corresponding to ?1 and ?2, respectively.
 
x1  = 
 
 
 
x2  = 
 
 
 
   
STEP 3: Since the matrix does not have linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.

linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.

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