21-06-2024 16:59

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Tags : mathematics linear algebra Linear Equations

System of linear equations in matrix

Definitions, Formulae and Theory A linear system of m equations in n unknowns $x_1,x_2,...,x_n$ is a set of equations of the form: $a_{11}{x}_1+a_{12}{x}_2+...+a_{1n}{x}_n=b_1$ $a_{21}{x}_1+a_{22}{x}_2+...+a_{2n}{x}_n=b_2$ $...$
$a_{m1}{x}_1+a_{m2}{x}_2+...+a_{mn}{x}_n=b_m$

This is called a System of Linear Equations. It is called “linear” because each variable $x_i$ is of first degree only.

The given system can also be written in matrix form as: $[A][X]=[B]$

where:

• A is the matrix of coefficients
• X is the matrix of unknown variables
• B is the matrix of constants

If B = 0, then the system is homogeneous. If B ≠ 0, then the system is non-homogeneous.

The values of unknowns form a solution set of the given system, satisfying all the equations.

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