I am taking a basic LA course in uni and in a recent quiz, which was in the context of linear systems of equations and solving them through the reduction algos, this happened.
One of the questions asked in the quiz was what the leading entry(the actual value of said leading entry) of a row in an augmented matrix was, in this case the question asked for the leading entry on row2.
the attached augmented matrix was something like this:
'*' represents a real number there were no zero rows and the system was consistent. row1,col1 was non zero. The question asked what the leading entry of the second row (row 2)was. row2,col1 was non zero and row2,col2 was non zero.
now here's where I am mixed up, according to the source material this is the definition of a leading entry def1 but when talking about reduced echlon forms and pivot positions, pivot positions are defined as def2
here the author pic1 zeros out row2,col1 since ro1,col1 is a leading entry that works out to be a pivot position later on.
I thought to myself since row reduction to reduced echlon form doesn't change pivot positions and since pivot positions will refer to leading entries in the original matrix surely row2,col2 is the leading entry of row2 discarding the fact that row2,col1 is non zero and is the left most non zero element in its respective row.
At the time I answered the value of row2,col2 as I thought this was the most logical.
I haven't yet received my mark, so that's why I am not asking my teacher :P
Did I answer correctly? Was I correct in assuming what I assumed based on the definitions? Also I think it's relevant that English isn't my first language so please go easy on me :OO