###
consistent system

if a system has at least one solution

occurs when lines intersect

###
inconsistent system

a system with no solutions

occurs when lines are parallel

###
dependent system

a system with infinite solutions

occurs when two lines overlap

###
linear programming

purpose is to find optimum solutions given a list of restrictions/limitations by graphing and finding points

###
constraints

expressed as a system of inequalities in a linear programming problem

###
feasible region

represents the set of all possible production points under the limitations/constraints

###
objective quantity

profit or cost equation

###
linear programming theorem

the maximum or minimum values always occur at the vertices (corner points) of the feasible region

###
the maximum or minimum values always occur at the vertices (corner points) of the feasible region

linear programming theorem

###
matrix

a rectangular arrangement of numbers

table that is always represented by a capital letter

###
linear combination/elimination

method of solving two variable equations by getting rid of one of the variables

process usually includes multiplying one or both of the equations by a number

###
scalar

another word for number

###
Gaussian elimination

method for solving matrix equations by A*X=B

###
Triangular form

method of solving three variable systems by eliminating one variable at a time then re-entering values into the equations

x+y+z =

y+z=

z=

###
coefficient matrix

matrix of a matrix equation that has the numbers that come directly before the variables

Represented by A

###
unknown matrix

matrix of a matrix equation that has x y and z

represented by x

###
constant matrix

matrix of a matrix equation that has the answers to the equation (=______)

Represented by the letter B

###
matrix equation

x= A⋅1 *B

has a coefficient, unknown and constant matrix

###
dimensions of a matrix

row by column

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