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We investigate a system of coupled non-homogeneous linear matrix differential equations. By applying the diagonal extraction operator, this system is reduced to a simple vector-matrix differential equation. An explicit formula of the general solution is then obtained in terms of matrix convolution product, Hadamard product, and elementary matrix functions. Moreover, we discuss certain special cases of the main system when initial conditions are imposed.

Solving Non-Homogeneous Coupled Linear Matrix Differential Equations in Terms of Matrix Convolution Product and Hadamard Product