How to create educational linear algebra animations?

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I'm looking to create animations for a linear algebra course. I need things like writing and changing equations, including matrices, plotting of 2- and 3-dimensional axes with points, vectors, lines and planes, and so on. The intention is to incorporate the animations into a separate video, to demonstrate and visualize what's being said.

How can I go about creating such animations? I'm ideally looking for a free solution.

I'm aware of 3Brown1Blue's youtube channel and vPython package, but I'm looking for other options. Mostly because I don't like working with vPython.

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