SystemsOfEquationsGaussianElimination

# Systems of equation

A polynomial equation of degree 1 with one or several unknowns is called a **linear equation**:

All the linear equations have this form:

a_{1}x_{1} + a_{2}x_{2} + …..+ a_{n}x_{n} = b

where a_{1},a_{2},…, a_{n},b are real numbers and x_{1}, x_{2}, ….., x_{n} are unknowns or variables

If b = 0 it is called a

**homogeneous equation**.A

**solution of the equation**is a set of values of the variables, x_{1}= k_{1}, x_{2}= k_{2},…., x_{n}= k_{n}, which converts the equation into a numerical equality.Examples:

A

**system of m linear equations with n unknowns**is a set of m linear equations with n unknowns given together with the target of determining the common solution/s of all of them. It has the form:Where x

_{1},x_{2},…….x_{n}are the variables and a_{ij}, b_{i}are real numbers, i = 1,2….m, j = 1,2,….nExamples:

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