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4.4 Problem 11.  Does anyone have advice as to how this problem should be approached?  It isn't a system of equations, so how do we get the eigenvalues/vectors?
 
4.4 Problem 11.  Does anyone have advice as to how this problem should be approached?  It isn't a system of equations, so how do we get the eigenvalues/vectors?
  
                 REPLY: Set y = y1, and y2 = y1'.  Then, you will have a system.
+
                 REPLY: Say that y = y1, and y2 = y1'.  Then, you will have a system.
 
   
 
   
 
[[2010 MA 527 Bell|Back to the MA 527 start page]]  
 
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Revision as of 18:11, 23 September 2010

Homework 5 collaboration area

4.4 Problem 7. Can anyone provide some guidance on finding the Eigenvector for the imaginery eigenvalues in this problem? I am stuck trying to get the matrix to row reduce.

Re: 4.4 Problem 7: First you get the matrix that represents the differential equation: [[0 -2],[8 0]]. Solve the determinant for det(A - Lambda*I) = 0 = Lambda^2 + 16. Then solving for lambda, we obtain purely imaginary eigenvalues. When plugging in the eigenvalues, the trick to row reducing them (to get a bottom row of 0's) is to multiply by "i" and then divide out the constants (be careful to note that i^2 = -1). This should get you the eigenvectors.

4.4 Problem 11. Does anyone have advice as to how this problem should be approached? It isn't a system of equations, so how do we get the eigenvalues/vectors?

                REPLY: Say that y = y1, and y2 = y1'.  Then, you will have a system.

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