Estimate the number of steps that LUP algorthim takes to com

Estimate the number of steps that LUP algorthim takes to compute the determinant of  n x n matrix.

Solution

The complexity of LUP decompostion algorithm to compute determinant of nxn matrix is O(n^3).

means there n^3 operations or instructions are need to execute to compute determinant.

each instrution is a step, hence there n^3 steps are required to compute determinant of nxn matrix

example: for a 3x3 matrix it takes 3^3 = 27 steps to compute determinant