#### Study sets matching "algebra linear systems"

#### Study sets matching "algebra linear systems"

Graphically, a system of equations has…

Graphically, a system of equations has…

The three possible solutions for a syst…

A system has infinite solutions if:

They are parallel lines. They never intersect so there's no wa…

at the point of intersection. The point where lines have a com…

- no solution... - infinite solutions ... - a unique solution

The equations are equal.... Same slope and y-intercept.

Graphically, a system of equations has…

They are parallel lines. They never intersect so there's no wa…

Graphically, a system of equations has…

at the point of intersection. The point where lines have a com…

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pai…

a system of linear equations that has an infinite number of so…

the use of addition or subtraction to eliminate one variable a…

a system of equations with no ordered pair that satisfies both…

consistent

a system of linear equations that has at least one ordered pai…

dependent

a system of linear equations that has an infinite number of so…

elimination method

linear inequality

solution of a system of linear inequali…

solution of a system of linear equations

solving systems by adding or subtracting equations to eliminat…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true. […

a set of values that make all equations in a system true. [p.…

elimination method

solving systems by adding or subtracting equations to eliminat…

linear inequality

an inequality in two variables whose graph is a region of the…

system of linear equations

solution of a system of linear equations

substitution method

system of linear inequalities

two or more linear equations with the same variables

the ordered pair that makes both equations true at the same ti…

one equation is solved for one of the variables then the the e…

two or more linear inequalities with the same variables

system of linear equations

two or more linear equations with the same variables

solution of a system of linear equations

the ordered pair that makes both equations true at the same ti…

System of linear equations

Point of intersection

Solution of a linear system

Substitution method

Two or more linear equations in the same variables, x and y.

The ordered pair (a, b) that lies on the graphs of two or more…

An ordered pair (x, y) that makes each equation in the system…

Solving for one variable and substituting the result in the se…

System of linear equations

Two or more linear equations in the same variables, x and y.

Point of intersection

The ordered pair (a, b) that lies on the graphs of two or more…

System of linear equations

Point of intersection

Solution of a linear system

Substitution method

Two or more linear equations in the same variables (x,y)

Ordered pair (a,b) that lies on the graphs of two or more equa…

Solving for one variable and substituting the result in the se…

Solving for one variable and substituting the result

System of linear equations

Two or more linear equations in the same variables (x,y)

Point of intersection

Ordered pair (a,b) that lies on the graphs of two or more equa…

Optomizing

Steps For Optomizing

No Solution

Infinitely Many Solutions

Maximize profit, minimize cost

1. Define variables (always first)... 2. Write system of inequali…

Inconsistent

Consistent, Dependent

Optomizing

Maximize profit, minimize cost

Steps For Optomizing

1. Define variables (always first)... 2. Write system of inequali…

consistent system

dependent system

elimination method

inconsistent system

a system of equations or inequalities that has at least one so…

a system of equations that has infinitely many solutions

a method used to solve systems of equations in which one varia…

a system of equations or inequalities that has no solution

consistent system

a system of equations or inequalities that has at least one so…

dependent system

a system of equations that has infinitely many solutions

consistent system

dependent system

elimination method

inconsistent system

a system of equations or inequalities that has at least one so…

a system of equations that has infinitely many solutions

a method used to solve systems of equations in which one varia…

a system of equations or inequalities that has no solution

consistent system

a system of equations or inequalities that has at least one so…

dependent system

a system of equations that has infinitely many solutions

Function

Function Notation

Input

Output

A relationship where each input has exactly one output.

If x is input and y is the output, then the function notation…

A number in the domain of a function. ... The independent variabl…

A number in the range of a function.... The dependent variable.

Function

A relationship where each input has exactly one output.

Function Notation

If x is input and y is the output, then the function notation…

CHORD

CIRCLE

LINEAR EQUATION IN STANDARD FORM

MIDPOINT

A LINE SEGMENTWITH END POINTS ON A CIRCLE.

A GEOMETRIC FIGURE CONSISTING OF ALL POINTS P THAT ARE FIXED D…

THE FORM AX+BY=C OF A LINEAR EQUATION.

A POINT ON A LINE SEGMENT THAT IS EDUIDISTANT FROM THE END POI…

CHORD

A LINE SEGMENTWITH END POINTS ON A CIRCLE.

CIRCLE

A GEOMETRIC FIGURE CONSISTING OF ALL POINTS P THAT ARE FIXED D…

Scalar multiplication

Standard Basis in Rn

Closed under addition

Closed under scalar multiplication

Multiplication of vectors by t, such that it becomes t(v1), t(…

Denoted by

**e**n, [1, 0, 0, 0...0] to the nth number. So in R3,…Two vectors, when added together, are still in the same subspa…

When a vector is multiplied by a scalar, it's still in the sam…

Scalar multiplication

Multiplication of vectors by t, such that it becomes t(v1), t(…

Standard Basis in Rn

Denoted by

**e**n, [1, 0, 0, 0...0] to the nth number. So in R3,…solution of a system of linear inequali…

system of linear inequalities

Consistent

independent

a set of values that make all inequalities in a system true.

a set of two or more linear inequalities with the same variabl…

system of equations with at least one solution

system that has exactly one solution

solution of a system of linear inequali…

a set of values that make all inequalities in a system true.

system of linear inequalities

a set of two or more linear inequalities with the same variabl…

System of linear equations

Solve graphically

Solution to a system of linear equations

Infinite solutions

2 or more linear equations

Use a graph to find the solution

The point at which 2 linear equations intersect.

The number of solutions a system has when the graphs of the eq…

System of linear equations

2 or more linear equations

Solve graphically

Use a graph to find the solution

System of Equations

Linear System

Solution of a System

Consistent System

a set of 2 or more equations

a system with linear equations

the set of values of the variable that makes all of the equati…

a system with at least one solution

System of Equations

a set of 2 or more equations

Linear System

a system with linear equations

consistent system

dependent system

inconsistent system

independent system

A system of equation or inequalities that has at least one sol…

a system of equations that has infinitely many solutions.

a system of equations or inequalities that has no solution.

a system of equations that exactly one solution.

consistent system

A system of equation or inequalities that has at least one sol…

dependent system

a system of equations that has infinitely many solutions.

consistent system

elimination

independent system

objective function

a system of equations or inequalities that has at least one so…

a method used to solve systems of equations in which one varia…

a system of equations that has exactly one solution

the function to be maximized or minimized in a linear programm…

consistent system

a system of equations or inequalities that has at least one so…

elimination

a method used to solve systems of equations in which one varia…

Suppose we have a final solution set of…

How are two linear systems equivalent?

How do you solve a linear system?

A matrix with size 3x4 is: ____________…

infinite

They share the same solution sets

Replace the l.s. with one that is equivalent but "simpler", th…

augumented matrix of *

Suppose we have a final solution set of…

infinite

How are two linear systems equivalent?

They share the same solution sets

System of Equations

System of Inequalities

Consistent

Inconsistent

A set of equations with the same variables.

A set of two or more inequalities with the same variables

A system of equations that has at least one solution is consis…

A system of equations that has no solution.

System of Equations

A set of equations with the same variables.

System of Inequalities

A set of two or more inequalities with the same variables

elimination method

linear inequality

solution of a system of linear inequali…

solution of a system of linear equations

solving systems by adding or subtracting equations to eliminat…

an inequality in two variables whose graph is a region of the…

a set of values that make all inequalities in a system true.

a set of values that make all equations in a system true.

elimination method

solving systems by adding or subtracting equations to eliminat…

linear inequality

an inequality in two variables whose graph is a region of the…

linear equation

consistent system

inconsistent system

leading entry

An equation that can be written as a1x1 + a2x2 + ... = b; a1,…

Has one or infinitely many solutions

Has no solution

Leftmost non-zero entry in a non-zero row

linear equation

An equation that can be written as a1x1 + a2x2 + ... = b; a1,…

consistent system

Has one or infinitely many solutions

Suppose we have a final solution set of…

How are two linear systems equivalent?

How do you solve a linear system?

A matrix with size 3x4 is: ____________…

infinite

They share the same solution sets

Replace the l.s. with one that is equivalent but "simpler", th…

augumented matrix

Suppose we have a final solution set of…

infinite

How are two linear systems equivalent?

They share the same solution sets

When Ax=b has no solution,

Linear system is homogenous if

Is a homogenous solution consistent or…

Trivial solution

the solution set is empty

it is of the form Ax = 0 vector in matrix equation form.

ALWAYS consistent because you can always write down the soluti…

x = 0; of Ax = 0

When Ax=b has no solution,

the solution set is empty

Linear system is homogenous if

it is of the form Ax = 0 vector in matrix equation form.

Homogeneous Solution:

Trivial Solution:

Nontrivial Solution:

[THEOREM] The homogeneous equation Ax =…

Ax = 0; 0 is the zero vector.

the zero solution.

a nonzero vector x that satisfies Ax = 0.

the equation has at least one free variable.

Homogeneous Solution:

Ax = 0; 0 is the zero vector.

Trivial Solution:

the zero solution.