I'm having a hard time understanding what "rank" really means in terms of matrices.
For example, I've been asked to Find the rank and nullity of the matrix given below:
|0 1 2|
|0 1 0|
I understand a pivot element is the first nonzero element in the row, and every pivot below it needs to be further to the right than the previous pivot. But are numbers considered pivots even if you don't use them to eliminate something?
for example, the RREF of this matrix is:
|0 1 0|
|0 0 1|
I never used the 0 1 2 row to eliminate anything - yet we still consider the one in the row to be a pivot. Why?
What exactly is a pivot?