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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