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.
matrix element
Every item listed in a matrix is (one of these) of the matrix. They are identified by their position in the matrix.
row operation
On an augmented matrix, this is when any of the following occurs: switch two rows, multiply a row by a constant, or add one row to another.
