Matrix of a system of linear equations

For a system of $𝑛$ unknowns and $𝑚$ equations; given $𝐴$ is the $𝑛 \times 𝑚$ matrix containing the coefficients, $⃗ 𝐱$ is the column vector of unknowns, and $⃗ 𝐛$ is the column vector of results; a system may be represented as

𝐴 ⃗ 𝐱 = ⃗ 𝐛

e.g. the following system

3 𝑥 + 2 𝑦 = 5 2 𝑥 - 9 𝑦 = 0

can also be stated as

[322−15]\vtwo𝑥𝑦=\vtwo50

Augmented matrix

When solving systems of linear equations by, for example, Gaußian elimination, it is common to form the "augmented matrix" $[𝐶 | ⃗ 𝐛]$ . Using the example above

[325 2 - 15 0]

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