How to Play
Consider the standard basis vectors \(i = (1,0)\) and \(j = (0,1)\)
- Your goal is to drag and drop the green basis vectors (\(i'\) and \(j'\)) to apply a transformation on the grid that maps blue on to red
- It may be a rotation, reflection, or scaling, or all three
- \(i'\) acts on the \(x\) component of blue and \(j'\) acts on the \(y\) component of blue, together they form a \(2 \times 2\) matrix: \[A = \begin{bmatrix} i'_x & j'_x \\ i'_y & j'_y \end{bmatrix}\] The goal is to have \(Ax = b\) where \(x\) is the blue vector, \(b\) is the red vector, and the light blue vector is \(Ax\)
- Try to make the light blue (image) vector land on the red point
- Click solve to see one possible solution matrix (solutions are not unique)
