# How can I solve Image matrix homography?

I have a problem. I couldn't understand this question. I know homography formula. I implemented this formula for zero level of first image pyramid but I couldn't get second image pyramid points at zero level.

Can you explain this question

The following is a list of points on an image pyramid P and another list of points on another image pyramid P’.

Points on P

Point  x    y     level
A      16   64    0
B      4    10    1
C      16   4     2
D      20   8     0
E      8    4     2
F      8    16    1


Points on P’

Point  x    y     level
G      84   142   0
H      9    16    2
I      77   37    1
J      54   92    0
K      22   41    1


(x,y) coordinates are measured in the image with the given level. Level 0 is the largest image in the pyramid with width/height of each level k+1 equal to the half of the width/height of level k. If the two image pyramids are related by the homography matrix H at level 0.

$$\begin{bmatrix}0.5&2&20\\2&0.5&10\\0&0&1\end{bmatrix}$$

find which points are corresponding to each other with the relation p’ ≡ Hp