Consider a system of linear equations given by |z (t)=22+y |y' (t) = − 3x + 4y (a) Find the eigenvalues and eigenvectors

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Consider A System Of Linear Equations Given By Z T 22 Y Y T 3x 4y A Find The Eigenvalues And Eigenvectors 1 (56.09 KiB) Viewed 10 times

Consider a system of linear equations given by |z (t)=22+y |y' (t) = − 3x + 4y (a) Find the eigenvalues and eigenvectors of this system's coefficient ma- trix. (If the eigenvalues are complex, you only need to find an eigen- vector for one of the complex eigenvalues.) [4 marks] (b) Find the general solution of this system. If any, identify the straight- line solutions. [4 marks] (c) Sketch the nullclines (indicating the direction field on the nullclines) and phase portrait of this system. Classify the equilibrium solution(s) as a sink, source, saddle, spiral sink/source, or nodal sink/source. [4 marks]