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.]

PLEASE PROVIDE SCREENSHOTS OF WORKING PROGRAM AND ITS OUTPUT! (Every solution I've gotten there has been an error in the program, please make sure the program is running and send photos of the solution.)

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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!!!!!!!

Please do not copy and paste from another solution. :)