Information:
Gaussian elimination transforms a system into upper triangular form through row operations. The elimination process proceeds column by column, eliminating entries below the diagonal.
Consider the following modified Python code for Gaussian elimination:

def gauss_elim_v2(A, b):
n = len(A)
for k in range(n-1):
for i in range(k+1, n):
factor = A[i][k] / A[k][k]
for j in range(n):
A[i][j] -= factor * A[k][j]
b[i] -= factor * b[k]
return A, b

What is the consequence of using range(n) instead of range(k, n) in the innermost loop?

Question

Information: 
 Gaussian elimination transforms a system    into upper triangular form through row operations. The elimination process proceeds column by column, eliminating entries below the diagonal. 
Consider the following modified Python code for Gaussian elimination:

def gauss_elim_v2(A, b):
    n = len(A)
    for k in range(n-1):
        for i in range(k+1, n):
            factor = A[i][k] / A[k][k]
            for j in range(n):
                A[i][j] -= factor * A[k][j]
            b[i] -= factor * b[k]
    return A, b

What is the consequence of using  range(n)  instead of  range(k, n)  in the innermost loop?

Answer

Previous elimination results are corrupted by modifying already-processed columns.

Answer

Division by zero is triggered when accessing previously processed column entries.

Answer

Elements above the diagonal become non-zero, violating upper triangular form.

Answer

Redundant operations on already-zeroed entries occur but output remains correct overall.

Answer

The loop index exceeds the valid column range of the matrix, causing out-of-bounds memory errors.

Answer

Entries in the first    columns fail to be eliminated during the inner loop.

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Information: Gaussian elimination transforms a system into upper triangular...

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