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consistent system

if a system has at least one solution

occurs when lines intersect

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inconsistent system

a system with no solutions

occurs when lines are parallel

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dependent system

a system with infinite solutions

occurs when two lines overlap

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linear programming

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

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constraints

expressed as a system of inequalities in a linear programming problem

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feasible region

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

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objective quantity

profit or cost equation

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linear programming theorem

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

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

linear programming theorem

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matrix

a rectangular arrangement of numbers

table that is always represented by a capital letter

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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

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scalar

another word for number

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Gaussian elimination

method for solving matrix equations by A*X=B

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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=

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coefficient matrix

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

Represented by A

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unknown matrix

matrix of a matrix equation that has x y and z

represented by x

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constant matrix

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

Represented by the letter B

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matrix equation

x= A⋅1 *B

has a coefficient, unknown and constant matrix

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dimensions of a matrix

row by column

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