Question

Write a python program that can solve system of linear equations in three variables using input function. Paste your program in a word document or notepad. Note that I am using pycharm. please use a not really complex codes, thanks

Answer 1

# find determinant of 3 x 3 matrix
def determinant(matrix):
    d = matrix[0][0] * (matrix[1][1] * matrix[2][2] - matrix[2][1] * matrix[1][2]) \
        - matrix[0][1] * (matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0]) \
        + matrix[0][2] * (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]) 
    # return the result
    return d

# find solution using cramer's rule
def solution(coefficient):
    # extract matrix m from coefficient matrix
    m=[[coefficient[0][0], coefficient[0][1], coefficient[0][2]],\
    [coefficient[1][0], coefficient[1][1], coefficient[1][2]],\
    [coefficient[2][0], coefficient[2][1], coefficient[2][2]]]

    # extract matrix m1 from coefficient matrix
    m1=[[coefficient[0][3], coefficient[0][1], coefficient[0][2]],\
    [coefficient[1][3], coefficient[1][1], coefficient[1][2]],\
    [coefficient[2][3], coefficient[2][1], coefficient[2][2]]]

    # extract matrix m2 from coefficient matrix
    m2=[[coefficient[0][0], coefficient[0][3], coefficient[0][2]],\
       [coefficient[1][0], coefficient[1][3], coefficient[1][2]],\
       [coefficient[2][0], coefficient[2][3], coefficient[2][2]]]

    # extract matrix m3 from coefficient matrix
    m3=[[coefficient[0][0], coefficient[0][1], coefficient[0][3]],\
       [coefficient[1][0], coefficient[1][1], coefficient[1][3]],\
       [coefficient[2][0], coefficient[2][1], coefficient[2][3]]]
    
    # calculate determinant of each of the matrices
    det=determinant(m)
    det1=determinant(m1)
    det2=determinant(m2)
    det3=determinant(m3)

    if det!=0:
        # unique solution
        x=det1/det
        y=det2/det
        z=det3/det
        print("\nSolution:")
        print("Value of X: ",x)
        print("Value of Y: ",y)
        print("Value of Z: ",z)
    else:
        if det1==0 and det2==0 and det3==0:
            print("There are infinite solutions")
        elif det1!=0 or det2!=0 or det3!=0:
            print("There is no solutions")

# take input for coefficient matrix
def equations():
    # declare an 3 x 4 list
    coef = [x[:] for x in [[0]*4]*3]
    for i in range(3):
        print("Input for equation",i+1)
        coef[i][0]=float(input("Enter the coefficient of X: "))
        coef[i][1]=float(input("Enter the coefficient of Y: "))
        coef[i][2]=float(input("Enter the coefficient of Z: "))
        coef[i][3]=float(input("Enter D"+str(i+1)+": "))

    # show the equations
    print("\nThe linear equations are: ") 
    for i in range(3):
        print(coef[i][0],"X + ",coef[i][1],"Y + ",coef[i][2],"Z = ",coef[i][3])

    return coef
        

def main():
    # call function to take input
    coefficient=equations();
    # find solution
    solution(coefficient)

# driver code
if __name__ == "__main__":
    main()

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Input for equation 1
Enter the coefficient of X: 5
Enter the coefficient of Y: 7
Enter the coefficient of Z: 4
Enter D1: 15
Input for equation 2
Enter the coefficient of X: 3
Enter the coefficient of Y: 7
Enter the coefficient of Z: 2
Enter D2: 8
Input for equation 3
Enter the coefficient of X: 5
Enter the coefficient of Y: 9
Enter the coefficient of Z: 3
Enter D3: 6

The linear equations are: 
5.0 X +  7.0 Y +  4.0 Z =  15.0
3.0 X +  7.0 Y +  2.0 Z =  8.0
5.0 X +  9.0 Y +  3.0 Z =  6.0

Solution:
Value of X:  -8.1
Value of Y:  1.3
Value of Z:  11.6

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Note: If you have queries or confusion regarding this question, please leave a comment. I would be happy to help you. If you find it to be useful, please upvote.