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Matrices : Subspace and Dimension

I have worked out a transformation problem and assembled a matrix. I have shown my work on the transformation and created matrix in the attached file. At the end of my work I have five (5) short theory questions about subspaces and dimension. Please see attached file.


Solution Summary

Subspace and dimension are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.