Consider a 3 x 3 matrix A with eigenvalues L_i and corresponding linearly independent eigenvectors xi, i = 1,2,3. Suppose L1= L2. Choose the true statement from (i), (ii), (iii) below and give an explanation for your answer. (i) A can be diagonalized. (ii) A cannot be diagonalized. (iii) I need more information to decide.
Consider a 3 x 3 matrix A with eigenvalues L_i and corresponding linearly independent eigenvectors xi, i = 1,2,3. Suppose L1= L2. Choose the true statement from (i), (ii), (iii) below and give an explanation for your answer. (i) A can be diagonalized. (ii) A cannot be diagonalized. (iii) I need more information to decide.
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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Consider a 3 x 3 matrix A with eigenvalues L_i and corresponding
linearly independent eigenvectors xi, i = 1,2,3. Suppose L1= L2.
Choose the true statement from (i), (ii), (iii) below and give an
explanation for your answer.
(i) A can be diagonalized.
(ii) A cannot be diagonalized.
(iii) I need more information to decide.
Expert Solution
Step 1
I will explain through an example by considering 2x2 as well as 3x3 matrix .we determine whether or not the following matrices are diagonalizable.
If it is diagonalizing matrix, we find P and a diagonal matrix D such that P-1AP=D
A.) 
B.) 
c.) 
d.)
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