Chpt. 3, Linear Systems Flashcards
system of equations
A set of two or more equations using the same variables.
linear system
A set of two or more linear equations that use the same variables.
solution of a system
A set of values for the variables that makes all the equations in the system true.
inconsistent system
A system of equations that has no solution(s). For example, the equations y = x + 1, and y = x -1.
consistent system
A system of linear equations is consistent if it has at least one solution.
independent system
A system of linear equations that has a unique solution.
dependent system
A system of linear equations that does not have a unique solution.
- intersecting lines
- coinciding lines
- parallel lines
- one solution, consistent, independent
- infinitely many solutions, consistent, dependent
- no solution, inconsistent
equivalent systems
Systems that have the same solutions.
linear programming
A method of finding the minimum of maximum value of some quantity, given a set of constraints.
constraint
Restrictions on the variables of the objective function in a linear programming problem.
feasible region
A region that contains all the values that satisfy the constraints on the objective function.
objective function
A model of the quantity that you want to make as large or as small as possible.
vertex principle of linear programming
If there is a maximum or a minimum value of the linear objective function, it occurs at one or more vertices of the feasible region.
matrix
A rectangular array of numbers written within brackets.
