A matrix A sends every point x to Ax. Set the four entries (type them, drag the sliders, or pick a preset) and watch the grid deform. The red and green arrows are the images of the basis vectors e1, e2: they are exactly the two columns of A. Set x by typing or by dragging the gray vector, and see its image Ax.
Type any numbers, or use the sliders below.
Type the components, or drag the gray arrow on the plot.