In this diagram illustrated in the Week 3 lecture #1, how are the linearly transformed coordinates (-2, 3) (blue image) mapped to coordinates (-3, 4) (yellow image)? I cannot see how the image on the right is a graph of (-3, 4) as shown by the black lines traversing across the Y and X axes in the transformed plane.
Dear @Hartej_Dhiman
So, you can see the transformation in two ways:
- Visually: This is what the image on blue and orange is showing. If you go two positions to the left and then three up on the blue plane you get to -2,3 and if you do the same (two positions to the left and three up) but on the orange plane you will get to the point that in the blue plane would me called -3,4 (you can see that the animation shows the original grid behind the orange plane, like a shadow, and if you count the dot on that plane it will be -3,4)
- Mathematically: You multiply the coordinates/vector -2,3 by the matrix in order words this:
I hope this explains what the animation is showing.
Thank you. It did help me understand the mapped vector after the translation. As a recommendation for improvement that might benefit other students, it would help it immediately become clear if the orange figure also had colored set of lines (perhaps dark red) on the original, blue grid that extended leftwards from (0,0) to (0, -3) and then from (-3, 0) to (-3, 4). Or at least a line representing the vector (-3, 4) connecting (0,0) and (-3,4) on the blue grid.