1. Consider the 2-dimensional system of linear equations X' = egin{bmatrix} 3 & -1 \ 1 & 1 end{bmatrix} X (a) Determine the eigenvalues of the system. Note that it is a repeated eigenvalue. Find all corresponding eigenvectors. (b) Classify the equilibrium point of the system (by type and stability). (c) Find the nullclines for the system and determine where in the phase plane solutions are traveling Up/Down and Left/Right. (d) Using information from the eigenvalues and eigenvectors and nullclines, draw a phase portrait for the system.
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Eigenvalues: To find the eigenvalues of the system, we need to solve the characteristic equation, which is given by det(A - Ī»I) = 0, where A is the matrix of coefficients of the system, I is the identity matrix, and Ī» are the eigenvalues. The solution to this Show moreā¦
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