# Need a transformation matrix to convert to new base vectors

I was searching for a solution, but can't find anything I can use with my superficial knowledge.

So, I have vector A, vector B & vector C. I want to convert the space to base vectors A & B (in a 2-dimensional space, of course), so that I could express C as their sum.

How can I do this? I could just calculate the x & y in C = x*A + y*B through scalar products, but I'd prefer matrix forms to avoid checking for zero denominators etc.

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