Building and Solving Linear Equations

The linear algebra module of NumPy, linalg, provides a number of functionalities, including the ability to solve systems of linear equations. This is done using the matrix method.

Suppose we have the following system of linear equations:

$2x+3y+z=17$

$3x+4y+2z=25$

$x+y-z=6$

We need to convert these to the form $AX=b$ and solve the equation for $X$.

$\begin{bmatrix}2 & 3 & 1 \\3 & 4 & 2 \\1 & 1 & -1 \end{bmatrix} \begin{bmatrix}x \\y \\z \end{bmatrix} = \begin{bmatrix}17 \\25 \\6 \end{bmatrix}$