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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:

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

Out[1]:

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]

Out[2]:

9.0