First Example. We will perform two sample problems. The first is outlined below. Suggested reading is Numerical Methods for Engineers, Fifth Edition by Chapra and Canale.
import numpy as np
#Solve the following set of three linear equations
# 4x + 3y + 2z = 25
# -2x + 2y + 3z = -10
# 3x - 5y + 2z = -4
A = np.array([[4, 3, 2], [-2, 2, 3], [3, -5, 2]])
B = np.array([25, -10, -4])
X = np.linalg.inv(A).dot(B)
print(X)
#Dot product of the inverse of matrix A, and matrix B.
#Output [ 5. 3. -2.]
# x, y, z equals respectively 5, 3, -2
Second Example. Solve the set of five linear equations below. Note that we must display the matrix in the proper form for the numpy algorithm. The Output is shown in the comments.
# Solve the following five linear equations
# 6v - x = 50
# -3v + 3w = 0
# -w + 9x = 160
# -w - 8x + 11y -2z = 0
# -3v - w + 4z = 0
#The 5 equations can be displayed as:
# 6v + 0w - 1x + 0y + 0z = 50
# -3v + 3w + 0x + 0y + 0z = 0
# 0v - 1w + 9x + 0y + 0z = 160
# 0v - 1w - 8x + 11y - 2z = 0
# -3v - 1w + 0x + 0y + 4z = 0
import numpy as np
A=np.array([[6,0,-1,0,0],[-3,3,0,0,0],[0,-1,9,0,0],[0,-1,-8,11,-2],[-3,-1,0,0,4]])
B=np.array([50,0,160,0,0])
# Dot product of the inverse of matrix A, and matrix B
X=np.linalg.inv(A).dot(B)
print(X)
#Output [11.50943396 11.50943396 19.05660377 16.99828473 11.50943396]
