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consistent system

if a system has at least one solution

occurs when lines intersect

occurs when lines intersect

inconsistent system

a system with no solutions

occurs when lines are parallel

occurs when lines are parallel

dependent system

a system with infinite solutions

occurs when two lines overlap

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

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

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=

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

Represented by A

unknown matrix

matrix of a matrix equation that has x y and z

represented by x

represented by x

constant matrix

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

Represented by the letter B

Represented by the letter B

matrix equation

x= A⋅1 *B

has a coefficient, unknown and constant matrix

has a coefficient, unknown and constant matrix

dimensions of a matrix

row by column