Gaussian Elimination rules - apply to rows only?

[ZedCar]

Homework Statement

In this video;

the uploader states at 0:47 that there are three rules.

1. Can swap rows
2. Can multiply a row by a constant
3. Can add a multiple of one row to another

Do these rules apply only to rows? Can they be applied to columns? The uploader has not stated this.

Thank you.

Homework Equations

The Attempt at a Solution

 

[HmBe]

Think it depends on what you're trying to do via GE.

If you have 2 equations,

2x+3y=1
4x+2y=11

Then you will have a matrix

2 3
4 2

multiplied by

x
y

will be equal to

1
11

Finding solutions to this, it clearly makes no sense to multiple columns by a scalar, as this will change the equations, and the solutions.

However, if you're trying to find a determinant, then I think you can apply the same rules to columns, as you're allowed to transpose the matrix.

 

[ZedCar]

Thank you HmBe.