Question: I need help in this question its due in 12 hrs . This is abstract Algebra course and the book is abstract algebra structure and

I need help in this question its due in 12 hrs . This is abstract Algebra course and the book is abstract algebra structure and application by david R Finston and Patrick J.

I will really appreciate help.Thanks

1. Let C be the code (of length n) of solutions to a matrix equation Ax = ll. Dene a relation on the set E of words of length}: by u E vmod C if u + v E C. Prove that this is anequivalence relation, and that for any word w, the equivalence class of w is the coset C + w

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