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For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.
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Proof that bases etc. exist in early linear algebra course?
I do not really know what is the level of the course and what else is in the syllabus, but there are many excellent books in linear algebra that cover abstract vector spaces almost painlessly.
A good …