Let S and T be the subspaces of generated by the matrices and
respectively, where
and
Determine dim(s) and dim(T).
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Now, the problem I have with this is that, I know how to find a basis (and hence a dimension) for vector spaces over real-number fields (i.e. ), by stacking the spanning vectors and reducing the matrix to echelon form, etc. But here we have matrices. How can I stack them?