Question

In rref,
1)pivot rows are independent.
2)pivot columns are independent.
If the above two statements are true, Can someone please explain me why? I probably understand why rows are independent, but I am not sure why pivot columns are independent.

Answer 1

by elimination we find pivot column and independent columns are found as pivot column.for a invertible matrix (columns are independent ) by elimination we find all columns as pivot columns.

Answer 2

Thanks..

Answer 3

,because the form of the matrix is echelon. And every column and every row can just have one pivot.