(a) Show that n operations are needed to create the first leading 1: (Why don’t...

(a) Show that n operations are needed to create the first leading 1:

(Why don’t we need to count an operation for the creation of the leading 1?) Now show that n operations are needed to obtain the first zero in column 1:

(Why don’t we need to count an operation for the creation of the zero itself?) When the first column has been “swept out,” we have the matrix

Show that the total number of operations needed up to this point is n 1 (n 2 1)n.

(b) Show that the total number of operations needed to reach the row eche lon form