# Transformation matrix

I'm kinda confused about transformation matrixes.

If I have [xw1,xw2,yw1,yw2] and [xv1,xv2,yv1,yv2].

What is the transformation matrix that makes (xw, yw) to (xv, yv)?

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Please, explain again your problem and fix some notations. –  Sigur Nov 11 '12 at 0:25

## 1 Answer

Solve these: $$\pmatrix{a&b\\c&d}\cdot\pmatrix{xw_1\\xw_2} =\pmatrix{xv_1\\xv_2}$$

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a = 1/xw1 b = xv1/xw2 c = 1/xw1 d = xv2/xw2. Is this correct? But does that solve my problem? :S –  alb Nov 11 '12 at 9:15
No, not correct. Matrix multiplication is a bit more complicated. LHS looks like: $\pmatrix{a\cdot xw_1+b\cdot xw_2 \\ c\cdot xw_1 + d\cdot xw_2}$, the RHS don't change. So it means $a\cdot xw_1+b\cdot xw_2 = xv_1$ and $c\cdot xw_1 + d\cdot xw_2 = xv_2$. And similarl for the $y$'s. –  Berci Nov 11 '12 at 11:27
Yeah that's what I did. But I thought I had to fill in a, b, c and d to get the RHS. But I think I'm kinda confused. Is the principle the same as my problem? –  alb Nov 11 '12 at 12:02