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For estimation purposes, it is useful to consider functions with various levels of smoothness and boundedness. One such space of functions is Sobolev space. A useful result when considering such a collection is whether it is possible to extend the space from a specific domain to all of space. This result is known to work for scalar weighted Sobolev space on very general domains. In this work, these results are further expounded upon and generalized for vector valued functions in a matrix weighted setting."