Let's prove the uniqueness of row echelon form (Suppose we already knew existence)(adsbygoogle = window.adsbygoogle || []).push({});

First, for any m*n matrix A, think about homogeneous equation AX=0.

Obviously, AX=0 has a solution X=0, so its solution set is not empty.

And A's row echelon form has same solution set. So if there are more than 2 row echelon

forms, it's contradiction because it means AX=0 has more than 2 solution set.

I don't know where's the error in this proof....

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

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

# What is the error in this proof of uniquness of row echelon form?

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