Move the [color=#0000ff]blue points[/color] to see the effects of a linear transformation in R^2.[br][br][color=#0000ff]e_1' [/color]and [color=#0000ff]e_2'[/color] = where the standard basis vectors e_1 and e_2 are transformed. [br]The matrix of the transformation will have columns e_1' and e_2'.[br][br][color=#0000ff]OLD[/color] = the point you want to transform.[br]The new point is NEW = T(OLD).[br]The red arrows show that we move along e_1' and e_2' distances corresponding to the x- and y-coordinates of OLD. [br][color=#0000ff][br][/color][color=#0000ff]A, B, C, D[/color] = four points that determine a quadrilateral; move them around to see how the transformation changes its shape (transformed points A', B', C', D' form a new quadrilateral).