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I really need a good book with some solved exercises about Linear Algebra and Affine Geometry (orthonormal basis, rotations, etc.). I want to understand the algorithms to solve that kind of problems but I can't understand the theory, it's too unclear and I think that some exercises can help me a lot. Thank you!

EDIT: I want a book which present a lot of exercises with complete solutions, especially to prepare for exams and for better understanding

EDIT 2 : I really appreciate if you can recommend a book which contains : system of vectorial equations, rotation of basis, etc. I don't know why, but in general these concepts are missed from the books.

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Linear Algebra and its Applications by Gilbert Strang
Geometry by David A Brannan
Also Jim Hefferon, Linear Algebra. This is a well-known open-source textbook and has lots of good exercises.

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