Are the row vectors in a row reduced echelon matrix always independent?
I'm thinking that since the first row is the only row with a non-zero coefficient, then it must be independent of all the others. Following that logic, the second row must be independent of the others as well; since we proved that it was independent of the first one and the 2nd row has a non-zero coefficient in the 2nd spot which all the later rows don't have… and so forth.
Is this correct?
Best Answer
Deciding to answer my own question in case someone else on here is lost.
Independent vectors are vectors that cannot be written as a linear combination of each other. When we put a matrix into row reduced echelon form, we effectively see that if a row vector is not the zero vector, it can not be written in terms of the other vectors. As a result, row vectors in row reduced echelon form are independent of each other.