Editing Affine transformation (section)

====Example augmented matrix====
Suppose you have three points that define a non-degenerate triangle in a plane, or four points that define a non-degenerate tetrahedron in 3-dimensional space, or generally {{math|''n'' + 1}} points {{math|'''x'''{{sub|1}}}}, ..., {{math|'''x'''{{sub|''n''+1}}}} that define a non-degenerate [[simplex]] in {{mvar|n}}-dimensional space.  Suppose you have corresponding destination points {{math|'''y'''{{sub|1}}}}, ..., {{math|'''y'''{{sub|''n''+1}}}}, where these new points can lie in a space with any number of dimensions.  (Furthermore, the new points need not be distinct from each other and need not form a non-degenerate simplex.)  The unique augmented matrix {{mvar|M}} that achieves the affine transformation
<math display=block>\begin{bmatrix}\mathbf{y}_i\\1\end{bmatrix} = M \begin{bmatrix}\mathbf{x}_i\\1\end{bmatrix}</math>
for every {{mvar|i}} is
<math display=block>M =
\begin{bmatrix}\mathbf{y}_1&\cdots&\mathbf{y}_{n+1}\\1&\cdots&1\end{bmatrix}
\begin{bmatrix}\mathbf{x}_1&\cdots&\mathbf{x}_{n+1}\\1&\cdots&1\end{bmatrix}^{-1}.</math>