I am learning a matrix for neural networks and i have a doubt
So a transformation means what the coordinates of a vector will be on changing the value of x and y axis from 1(taken by default in plane R1) to some value .Like a point in a plane where x=1 and y=1 coordinates of a point is (3,2) so this means that 3 steps in x direction and 2 step in y direction .Now lets say in plane R2 we increase x by a factor of 2 and y by a factor of 5.So that same point in plane R2 with x=2 and y=5 will be (3×2,2×5) ie (6,10) Right?
This can also be represented as vector [[3],[2]] for point which is a 2X1 matrix and rows tell about value of x and y .
No we can multiply this by a factor of change ie x inc by 2 and y inc by 5 so result is [[32],[25]] result is [[6],[10]] ie 6 in x direction and 10 in y direction Right?
No i came across a problem when i saw a L(v)= AxV where a is a matrix and v is a vector so applying same case to get a result of a vector in form of 2X1 we put matrix A=[[2,0],[0,5]](increase in x and y in Plane R2) so here why we added a 0 after 2 and 0 before 5 ?
Q1)Just to get result in the form of 2X1 matrix or some other reason.
Q2)Will there be any impact of zeros on the matrix or not?

I am just confused please help