If A is a possible behaviour of a system, and B is another possibility. Your system behaves linearly if Y = A + B is another possible behaviour of the system. This is a common situation in physics.
Gilbert Strang is an undisputed giant in teaching Linear Algebra. Here you can find his lecture series for the introductory course at MIT.
A slightly different aproach to Linear Algebra is taken by Pavel Grinfeld. Whereas Strang is focused mainly on the mathematics that emerges when you restrict yourself to matrix representations, and the standard inner product—Grinfeld also extends the discussion to other types of vector-spaces (for instance functions as vectors), with various inner products defined on your space.
Finally, Grant Sanderson runs an excellent YouTube channel called 3Blue1Brown. His series Essence of linear algebra is a masterpiece in communicating an intuitive understanding of the central concepts in the field. You can support the channel here.