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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. | 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. | ||
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Re: 4.4 #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. | Re: 4.4 #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. | ||
Revision as of 11:08, 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 #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?
