What dx,dy mean and how it is made

and below is the pic of what i am referring to !!

image

and many times i have also seen some -1 0 1 0 , something like that as well , so what it means ?

okay i got that dx1,dy1… but many times -1 0 1 … something like that is written what it means then ??

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sir , here i can’t see any messages , please reply once again here !! thankyou sir !!

-1 means go up 1 row of the matrix
0 no change
1 means go down 1 row of the matrix