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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.

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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.

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