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.
4.5 Problem 1. What do we do about the y2 + y2^2? Specifically the square?
REPLY: factor our the y2: y2(1+y2). Set the function equal to zero (to find the critical points).
So you should get two solutions(y2 = 0 and y2 = -1). To find the corresponding values of y1, set the second function (y2' = 0, and solve). The two critical points should come out to be (0,0) and (0,-1).
