# Linear Algebra - Matrix Equation

A linear vector equation is equivalent to a matrix equation of the form : $$A.x=b$$

where:

$$A= \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix},\quad \bf{x}= \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix},\quad \bf{b}= \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}$$

A matrix equation is the same:

## Type

### Homogeneous

A set of a homogeneous linear system as a matrix equation $$Ax = 0$$

This formulation describes the Null Space of A

## Computation

Python Scipy can solve a linear system Ax = b with linalg.solve(A, b)