for this code how many row permutations were made :import numpy as np

from scipy.linalg import lu

# Generate a random symmetric matrix A

A $=$ np$.$random.rand$(100,100)$

A$\_$symmetric $=0\mathrm{.}5*($A $+$ A$.$T$)$ # Extract the symmetric part of A

# Compute LU factorization using scipy

P$,$ L$,$ U $=$ lu$($A$\_$symmetric$)$

# Reconstruct A

A$\_$reconstructed $=$ P @ L @ U

# Check the maximum absolute error between A$\_$symmetric and A$\_$reconstructed

max$\_$error $=$ np$.$max$($np$.$abs$($A$\_$symmetric $-$ A$\_$reconstructed$))$

print$("$Maximum absolute error:", max$\_$error$)$

# Check if A and A$\_$reconstructed are approximately equal

verification $=$ np$.$allclose$($A$\_$symmetric, A$\_$reconstructed$)$

if verification:

print$("$LU factorization verified."$)$

else:

print$("$LU factorization verification failed."$)$