In matrices, we justify row operations by drawing parallels with solving a system of equations i.e.:
1.Interchanging rows = Interchanging equations \
2.Adding one multiple of a row to another = Adding one multiple of an equation to another \
3.Multiplying all terms of a row by a constant = multiplying both sides of an equation by that constant.
Now, we can do much the same with columns as well. What's the logic supporting column operations? Can we draw a parallel to solving a system of equations for column operations as well? Thanks!