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Given X′=AX with X(t)=[x(t)y(t)], A=[23−4012−21] and X(0)=[3−4]. (a) Write the eigenvalues and eigenvectors of A...

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Given X′=AX with X(t)=[x(t)y(t)], A=[23−4012−21] and X(0)=[3−4]. (a) Write the eigenvalues and eigenvectors of A λ1= , V1= ⎡⎣⎢⎢ ⎤⎦⎥⎥ , and λ2= , V2= ⎡⎣⎢⎢ ⎤⎦⎥⎥ (b) Write the solution of the initial-value problem in terms of x(t),y(t) x(t)= y(t)=

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