Homework 16:Question 8 Suppose a system of differential equations can be written in matrix form asdxdtdtdzdt-Ay(t) =z(t) =Xwhere A is a 3 x 3 matrix.=YZIf A has eigenvalues 7, —1, 8 with corresponding eigenvectors0·00-2general solution to the system.(Use c₁ for terms involving eigenvalue 7, c₂ for terms involving eigenvalue –1, and c3 for termsinvolving eigenvalue 8.)x(t) =write the

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Suppose a system of differential equations can be written in matrix form as Г dx * 3* ** dt dt dz dt = A x(t) = = where A is a 3 x 3 matrix. = 8 S y(t) = = z(t) = Z If A has eigenvalues 7, -1,8 with corresponding eigenvectors -2 000 general solution to the system. (Use c₁ for terms involving eigenvalue 7, c₂ for terms involving eigenvalue -1, and c3 for terms involving eigenvalue 8.) I write the