Matrix vector v =[x, y, 1] multiplication to get v' =[x/y, y, w]

Question

How can I make a matrix (or multiple matrices) which, when multiplied by the vector v =[x, y, 1], I get the vector v' =[x/y, y, w] where w can be any number (w is not important, the purpose is to get the x/y, y part)?

Answer 1

Just use this 3x3 Matrix(after the first 3 numbers, and after six numbers a new matrix line starts, I am new to this page and can't use formatting yet): M=[1/y,0,0; 0 ,1,0; 0 ,1,w]