//To mathwonk
So, you mean this is the correct proof? (inspite lack of explain...)
I wondered why so many linear algebra books don't prove it in this way... (most of them prove it by using linear transformation or concept of vector space...)
So I thought it maybe wrong proof... it's so...
Let's prove the uniqueness of row echelon form (Suppose we already knew existence)
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...
Hello, I have a question about topology.
If X is a path-connected space then is it also true that closure X is path-connected?
I think it's obvious, but I can't solve it clearly...