PYTHON CODE DEBUGGING AND MODIFICATION

The below code is used for solving a system of linear equations using Gaussian Elimination:

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import numpy as np

# Define the matrix A and vector b

A = np.array([[1, 0, 2], [2, -1, 3], [4, 1, 8]])

b = np.array([1, -1, 2])

# Combine matrix A and vector b into a single augmented matrix C

C = np.column_stack((A, b))

# Initialize the success parameter E to 1

E = 1

# Get the size of the matrix

n = C.shape[0]

# Iterate over each column j

for j in range(n):

# Find the index of the row with the maximum absolute value in column j

p = np.argmax(np.abs(C[j:, j])) + j

# If the maximum value is 0, set E to 0 and exit

if C[p, j] == 0:

E = 0

break

# If the pivot is not in the j-th row, swap the rows

if p != j:

C[[j, p], :] = C[[p, j], :]

# Eliminate the entries below the pivot in column j

for i in range(j+1, n):

C[i, :] -= (C[i, j]/C[j, j]) * C[j, :]

# Check if a unique solution was found

if E == 1:

# Initialize the solution vector x with zeros

x = np.zeros(n)

# Back-substitution to solve for x

for j in range(n-1, -1, -1):

x[j] = (C[j, -1] - np.dot(C[j, j+1:n], x[j+1:n])) / C[j, j]

# Print the solution

print("The solution is: ", x)

else:

print("The algorithm failed to find a unique solution.")

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DEBUGGING:

I am getting an error when I run it into Python: C[i, :] -= (C[i, j]/C[j, j]) * C[j, :] numpy.core._exceptions._UFuncOutputCastingError: Cannot cast ufunc 'subtract' output from dtype('float64') to dtype('int64') with casting rule 'same_kind'

It should be producing:

The solution is: [-1. 1. 0.]

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MODIFICATION:

Create a new Python file and modify the code to compute the matrix determinant.

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THANK YOU!!!!! If your solution helps I will upvote!!!!!!!