The Pseudocode for Gaussian elimination for a n by n system

The Pseudocode for Gaussian elimination for a n by n system, Ax=b, is shown below Following the pseudocode above, how many loops are required to complete the forward elimination? Please also provide the formula a for n times n system for forward elimination. Following the pseudocode above, how many loops are required to complete the backward substitution? Please also provide the formula a for n times n system for backward substitution.

Solution

1)

(n-2)² + (n-3)²+.....+ (n-(n-1))²

n = 1 -> 0

n = 2 -> 0

n = 3 -> 1

n = 4 -> 5

n = 5 -> 14

2)

(n-3)+ (n-4) + .....+ (n-(n-1))

n < 4 -> 0

n = 4 -> 1

n = 5 -> 3

n = 6 -> 6