I understand why two of the three row operations do not change the solution set of a system:(adsbygoogle = window.adsbygoogle || []).push({});

1. Interchange two rows. (Doesn't make much difference in what order one decides to write down the linear equations does it?)

2. Multiply a row by a scalar. (This step doesn't change the solution set because e.g. writing 2x = 6 instead of x = 3 doesn't change the geometric situation at all)

It's the third one that's giving me trouble:

3. Replace one row with the sum of it and a multiple of another row.

Even though this is the key method of solving simultaneous equations, I cannot justify to myself that it doesn't change the solution set of a system. Can anyone shed light on this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Elementary Row Operations on Matrices

**Physics Forums | Science Articles, Homework Help, Discussion**