The MIT OCW (if it's Strang) is nice, but is more geared to engineers, focusing on matrix mechanics.
Although this is useful, if you are interested in a more rigorous, math treatment that will also be subsequently quite useful in further studies of algebra, I would recommend these two courses.
They both use "Linear Algebra Done Right" which (despite it's awful title) is widely used in math programs. These two websites generously offer a great deal of very helpful material.
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