Time for action – solving a linear system

Let's solve an example of a linear system. To solve a linear system, perform the following steps:

1. Let's create the matrices A and b.

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

   The matrices A and b are shown as follows:

   

2. Solve this linear system by calling the solve function.

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

   The following is the solution of the linear system:

   Solution [ 29.  16.   3.]
   

3. Check whether the solution is correct with the dot function.

   print "Check\n", 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 (see solution.py).

import numpy as np

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

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

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

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