Definition

An algorithm for solving systems of linear equations. Transform a matrix to an upper triangular matrix using the elementary row operations.

Elementary Row Operations

Swapping two rows
Multiplying a row by a non-zero scalar
Adding a multiple of one row to another row

Examples

$1133111 1 - 1 5 ∣ ∣ ∣ 9135 \to r_{2} = r_{2} - r_{1} 100 3 - 2 2 1 - 2 2 ∣ ∣ ∣ 9 - 8 8 \to r_{3} = r_{3} + r_{2} 100 3 - 2 0 1 - 2 0 ∣ ∣ ∣ 9 - 8 0 \to r_{2} = - \frac{1}{2} r_{2} 100010 - 2 10 ∣ ∣ ∣ - 3 40$

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Gauss Elimination

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Elementary Row Operations

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