Time for action – solving a linear system

Solve an example of a linear system with the following steps:

  1. Create A and b:
    A = np.mat("1 -2 1;0 2 -8;-4 5 9")
print("A
", A)
b = np.array([0, 8, -9])
print("b
", b)

    A and b appear as follows:

    Time for action – solving a linear system
  2. Solve this linear system with the solve() function:
    x = np.linalg.solve(A, b)
print("Solution", x)

    The solution of the linear system is as follows:

    Solution [ 29.  16.   3.]
  3. Check whether the solution is correct with the dot() function:
    print("Check
", np.dot(A , x))

    The result is as expected:

    Check
[[ 0.  8. -9.]]

What just happened?

We solved a linear system using the solve() function from the NumPy linalg module and checked the solution with the dot() function. Please refer to the solution.py file in this book's code bundle:

from __future__ import print_function
import numpy as np

A = np.mat("1 -2 1;0 2 -8;-4 5 9")
print("A
", A)

b = np.array([0, 8, -9])
print("b
", b)

x = np.linalg.solve(A, b)
print("Solution", x)

print("Check
", np.dot(A , x))
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