Drag the red point to any location on the plane to serve as the image of e_1. Drag the blue point to any location on the plane to serve as the image of e_2. You have now set up a linear transformation T. The standard matrix A for the transformation T is given.
Now that you have fixed your linear transformation T, drag the orange point to set an input vector u. The vector in purple shows T(u). Below the horizontal axis is five lines of computation, all of which are equal to T(u).