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

consider that we have 2 equations and the lines of the 2 equations are in parallel and there’s no intersection. So we have ….

consider that we have 2 equations and the lines of the 2 equations intersect at only one point . So we have ….

consider that we have 2 equations and the lines of the 2 equations coincide. So we have ….

many points of intersection

the points on the common line

if the system has at least one solution we call it as

if the system has no solutions we call it as

if we have 3 planes and all of these planes are in parallel we have

if we have 3 planes and 2 of these planes are in parallel, we have