SystemsOfEquationsGaussianElimination

# Matrix associated to a system

A **matrix of m rows and n columns (mxn)** is an ordered table of numbers with the form:

← m^{th} row

2nd column ↑

Example:

is a 3x4 matrix

Then, each system

has two associated matrices:

Example:

Then the elementary operations are:

–To exchange two rows: R

_{i}↔ R_{j}–To substitute a row by a linear combination of all the rows:

R_{i}↔ k_{1}R_{1}+k_{2}R_{2}+…+k_{i}R_{i}+…k_{m}R_{m}, k_{i} ≠ 0, k_{j} are real numbers, j = 1, 2, ….m

**Exercise**. Find the associated matrices to these systems:

Solutions:

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