# 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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## 1 Answer

Let A=(a1,a2),B=(b1,b2),the matrix {{b2/(a1b2-b1a2),-b1/(a1b2-b1a2)},{a2/(a1b2-b1a2),-a1/(a1b2-b1a2)}} may help you.

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Thanks. I recall the linear algebra, it's the invertible matrix of (A B), and (a1b2 - b1a2) is the determinator. –  culebrón Mar 19 '12 at 10:35
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