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.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 5SE: Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why...
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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.) Determine whether or not the given matrices are di

B.) Determine whether or not the given matrices are di



c.) Determine whether or not the given matrices are di




d.)Determine whether or not the given matrices are di

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