## Question

###### Consider the 2-dimensional system of linear equations~=l- 'Jx Note that the coellicient matrix for this System contains prameter Determine the eigenvalues of the system in terms of The qualitative belnvior of the solutions depenks tlie vul of It changes fromn ollc ypve aiot hiet (olso whcn but (his poblem lccuses On the change 4 0). Classily tho euilibium point o the sstem (by type nnd stability) Wn 0.wlen Wa Determine the cigenvectors lor the system (in ters of &) for the cnses -4 <

Consider the 2-dimensional system of linear equations ~=l- 'Jx Note that the coellicient matrix for this System contains prameter Determine the eigenvalues of the system in terms of The qualitative belnvior of the solutions depenks tlie vul of It changes fromn ollc ypve aiot hiet (olso whcn but (his poblem lccuses On the change 4 0). Classily tho euilibium point o the sstem (by type nnd stability) Wn 0.wlen Wa Determine the cigenvectors lor the system (in ters of &) for the cnses -4 < 0 < and Determine tle nullclines for the system (in terms of a) tlie CAS whert Using information from the eigenvalues anch eigenvectors draw scquence of phase portraits for the systemt; for the follwoing situations; <0, 4 20 4 >

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