About

A linear vector equation is equivalent to a matrix equation of the form : <MATH>A.x=b</MATH>

where:

• A is an m×n matrix,
• x is a column vector with n entries,
• and b is a column vector with m entries.

<MATH> 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} </MATH>

A matrix equation is the same:

• as expressing a given vector (b) as a linear combination of other given vectors (A*x),
• and therefore as solving a system of linear equations

Articles Related

Computation

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

Documentation / Reference

• wiki/System_of_linear_equations