Linear algebra is a field of mathematical study that studies systems of linear equations and their solutions, vectors, and linear transformations. The matrix and its operations are also closely related to the linear algebra field.The linear equation can be expressed as a matrix. For example equation:

3×1 + 4×2 − 2×3 = 5
x1 − 5×2 + 2×3 = 7
2×1 + x2 − 3×3 = 9

can be expressed in the following teraugmentation matrix

aljabar linear 2017

Solution of linear equations in matrix form can be done through several ways, namely by elimination of Gauss or can also by way of Gauss-Jordan elimination. However, a system of linear equations can be solved by elimination of Gauss to convert the form of an accumulated matrix into a row-echelon form without simplifying it. This is called back-substitution.

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Solving Linear Equations with Matrices (Part 1)

The matrix can be said Echelon-line if it meets the following requirements:

In each row, the first digit other than 0 must be 1 (leading 1).
If there are rows that are all zero elements, they should be grouped in the final row of the matrix.
If there is a line leading 1 then leading 1 below it, the 1st should be more right than leading 1 on it.
If the column that has a leading 1 number other than 1 is zero then the matrix is called reduced-Echelon row

source: wikipedia.org/wiki/Aljabar_linear