Eigenvalue and Eigenvector of a matrix analyticaliy

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I have a matrix M which is defined as M(1,1)=, M(1,2)=, M(2,1)=, M(2,2)=-. Now I want to calculate the eigenvalue and eigenvector of the matrix analytically. For one can choose any wave-function which is depend on time and position such as . I am new to matlab please help regarding this.

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