Question

Hi guys, I have a question about zero rows of a reduced echelon form of a matrix. Why is the number of nonpivot columns the same as its zero rows of reduced echelon form? Thank you.

Answer 1

for example if if m x n matrix it means rows has zeroes then it means we will have
0xn=0,thats y columns will also have zeros.

Answer 2

It's true only if n=m. See section 3.6. rank = # pivot columns = # pivot rows. So #nonpivot columns = n - r, #nonpivot rows = m-r.

Answer 3

Thank you dhwagner. Your answer is really helpful. I will have a linear algebra midterm next Wed. Hope I won't screw it up.