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In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is Elementary Linear Algebra. The book should have at least the following things

-- An online homework system -- A good emphasis on proofs in the exercises -- Should introduce linear transformations earlier -- Some applications

Any recommendations would be greatly appreciated. Thank you for your help

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@NateEldredge But I thought that some questions relating to mathematical pedagogy (or "teaching maths in the trenches:) are on topic here? I am not sure about the present question –  Yemon Choi Sep 10 '13 at 19:40
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Check David Lay's "Linear algebra and its applications" taught with MyMathLab (online hw system). –  Igor Belegradek Sep 10 '13 at 20:59
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I agree with @YemonChoi -- this kind of question has been honored in the past without controversy. It's the type of question that professional mathematicians ask of one another. Perhaps a meta should be opened? –  Todd Trimble Sep 10 '13 at 21:49
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Meta: meta.mathoverflow.net/a/797/2926 –  Todd Trimble Sep 10 '13 at 23:19
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"Should introduce linear transformations earlier" --- earlier than what? –  Gerry Myerson Sep 11 '13 at 2:22
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