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Decide the stability of u 0 = Au for the following matrices: (a) A = " 2 3 4 5# . (b) A

Chapter 5, Problem 5.4.9

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QUESTION:

Decide the stability of u 0 = Au for the following matrices: (a) A = " 2 3 4 5# . (b) A = " 1 2 3 1 # . (c) A = " 1 1 1 2 # . (d) A = " 1 1 1 1 #

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QUESTION:

Decide the stability of u 0 = Au for the following matrices: (a) A = " 2 3 4 5# . (b) A = " 1 2 3 1 # . (c) A = " 1 1 1 2 # . (d) A = " 1 1 1 1 #

ANSWER:

Step 1 of 4

(a) It is given that   .

Find the eigenvalues as:

                                                 

Since the obtained eigenvalues are     different in signs so    is a saddle point and unstable.

 

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