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Systems of Linear Equations

Systems of Linear Equations

Systems of linear equations can be solved with arrays and NumPy. A system of linear equations is shown below:

8x + 3y -2z = 9
-4x + 7y + 5z = 15

$$ 3x + 4y - 12z = 35 $$ NumPy's np.linalg.solve() function can be used to solve this system of equations for the variables x, y and z.

The steps to solve the system of linear equations with np.linalg.solve() are below:

  • Create NumPy array A as a 3 by 3 array of the coefficients
  • Create a NumPy array b as the right-hand side of the equations
  • Solve for the values of x, y and z using np.linalg.solve(A, b).

The resulting array has three entries. One entry for each variable.

In [1]:
import numpy as np

A = np.array([[8, 3, -2], [-4, 7, 5], [3, 4, -12]]) b = np.array([9, 15, 35]) x = np.linalg.solve(A, b) x

array([-0.58226371,  3.22870478, -1.98599767])

We can plug the valuse of x, y and z back into one of the equations to check the answer.

x is the first entry of the array, y is the second entry of the array, and z is the third entry of the array.

x = x[0]

y = x[1]

z = x[2]

When these values are plugged into the equation from above:

8x + 3y -2z = 9

The answer should be 9.0.

In [2]:
8  x[0] + 3  x[1] - 2 * x[2]