The sketch below shows a transformation from the plane on the left to the plane on the right. Move [math]v[/math] to find its image [math]Mv[/math]. [br][br]This time, try to go backwards: Given an image, [math]Mv[/math], what was its preimage [math]v[/math]? [br][br]What is the preimage of [math](1, 0)[/math]? Of [math](0, 1)[/math]? Can you use these results to predict the preimage of [math](2, 3)[/math]? [br][br]Can you use these results to predict a matrix that will "undo" [math]M[/math]? We call such a matrix the [b]inverse[/b] of [math]M[/math].