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We derive the necessary and sufficient conditions for the solvability of a system of dual quaternion matrix equations (AX, XC, EXF) = (B, D, G) as well as their general solution expressions by means of the Moore-Penrose inverse and rank equalities. Then, the main conclusions of this paper are verified via a numerical example, and the applications of such equation systems to image encryption and decryption are investigated.
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Chen et al. (2026) studied this question.
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