I have an exercise that says if after the image move(that is the matrix and has the values x0,x1) or translation and then we rotate it for θ (Theta) degree and we scale it for (S0,S1) we have the matrix
T = $\begin{bmatrix}0.951623 & 0.443749 & -6.97686\\-0.401487 & 0.860992 & -2.29753\\0 & 0 & 1\end{bmatrix}$
Find x0,x1,θ and S0,S1
Write out the generic matrices for the three unknown transformations individually and compute their product. The brute-force way to obtain a solution is then to set this equal to $T$ and solve the resulting system of equations, but there’s a more systematic approach that might be more manageable.
Examine the generic transformation matrix that you computed above and look for patterns that might help you isolate some of the parameters. For example, what do you get when you square and add the first two elements of the first row? Does that suggest a way to compute one of the parameters of this transformation from $T$? Then, peel back the layers. Once you’ve found the scale factors, you can undo that part of the transformation and work on finding the rotation angle. After determining that, undo the rotation and you’ll have the translation.