Linear Systems Flashcards
To learn the key vocabulary for our chapter on Linear Systems (19 cards)
System of Equations
A set of two or more equations that use the same variables
Linear System
A set of two or more linear equations that use the same variables
Solution of a System
A value or set of values that for the variables that make the equations in the system true
Inconsistent System
A system of equations that has no solutions.
Example: y = x+2 and y = x-2
Consistent System
A system that has at least one solution
Independent System
A system that has a unique solution
Dependent System
A system that does not have a unique solution
Intersecting Lines
Have one solution, are consistent and independent
Coinciding Lines
Have infinite solutions, are consistent and dependent
Parallel Lines
Have no solution and are inconsistent
Equivalent Systems
Systems that have the same solutions
Linear Programming
A mathematical technique for maximizing or minimizing a linear function of several variables, 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
Matrix Element
Every item listed in a matrix is an element of the matrix. They are identified by their position in the matrix
Row Operation
The three operations that you can do with a matrix. They are row switching, row multiplication, and row addition
