I am doing linear algebra and I am a begginer. A thought struck on my mind that I need to work out that what is the relationship between pivots, pivot columns and linear independence?
As far as I perceived, if a matrix is in a row Echelon form, then the first non-zero entry (not necessarily 1) of each row is called its pivot.
Columns that contain the pivots - leading 1's of the rows - are called pivot columns.
Also, I'm aware for the fact that each non pivot column is linearly dependent. Are pivot columns linearly independent?
How pivot works for linear independence?