Recall that a line in 2-space (a rectangular xy-coordinate system) can be represented by an equation of the form

a1x1 + a2x2 + … + anxn = 0

A linear equation can involve products of variables

A linear equation can involve roots of variables

All variables in linear equation are to the power

trigonometric functions of variables can be involved in linear equations

logarithmic functions of variables can be involved in linear equations

exponential functions of variables (to the power which is bigger than 1) can be involved in linear equations

A finite set of linear equations is called a system of linear equations (Linear system)

variables in linear system are called unknowns

A solution of a linear system in n unknowns is a sequence of … numbers

the names of the variables are omitted. This notation allows us to interpret these solutions geometrically as points in two-dimensional and three-dimensional space . More generally a solution

with ordered n-tuple it is understood that all variables appear in the same order in each equation if n = 2 then the n-tuple is called an ordered pair, and if n = 3 then it is called an ordered triple

The double subscripting on the coefficients aij of the unknowns gives their location in the system

in The double subscripting on the coefficients aij the first coefficient indicates which unknown it multiplies

in The double subscripting on the coefficients aij the second coefficient indicates the equation in which the coefficient occurs

a12

Number of solutions that can occur in linear system