# Study sets matching "algebra linear systems"

Study sets

Diagrams

Classes

Users

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…

Augmented Matrix

Coefficient Matrix

Dimensions

Inconsistent System

A matrix that shows all coefficients and constants in a system…

A matrix that shows the coefficients of the variables in a sys…

This determines the number of rows and columns of a matrix

A system of equations with no solution

Augmented Matrix

A matrix that shows all coefficients and constants in a system…

Coefficient Matrix

A matrix that shows the coefficients of the variables in a sys…

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…

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,…Common Solution

Elimination

Substitution

System of Linear Equation

x-y coordinate of the graphical intersection of the linear equ…

The process of solving a linear system of equations by adding…

The process of solving a linear system of equations when one v…

One or more linear equations together in a problem

Common Solution

x-y coordinate of the graphical intersection of the linear equ…

Elimination

The process of solving a linear system of equations by adding…

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

system of equations

solution to a system of equations

parallel lines

right angles

a set of two or more equations that have the same variables

values that make both equations true

lines in the same plane that never intersect

angles with measure 90 degrees

system of equations

a set of two or more equations that have the same variables

solution to a system of equations

values that make both equations true

The number of solutions in a system of…

A system is said to be CONSISTENT if...

A system is said to be INCONSISTENT if.…

Echelon Form

None, One, or Infinitely Many

it has one or infinitely many solutions

it has no solution

1- rows of zeroes on the bottom, 2- each leading entry of a ro…

The number of solutions in a system of…

None, One, or Infinitely Many

A system is said to be CONSISTENT if...

it has one or 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…

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…

Theorem 4.7.2

Theorem 4.7.3

Theorem 4.7.4

Theorem 4.7.5

If x0 is any solution of a consistent linear system Ax=b, and…

Elementary row operation do not change the null space of a mat…

Elementary row operations do not change the row space of a mat…

if a matrix R is in row echelon form, then the row vectors wit…

Theorem 4.7.2

If x0 is any solution of a consistent linear system Ax=b, and…

Theorem 4.7.3

Elementary row operation do not change the null space of a mat…

Solving if something is in a Span

Span Theorems

Span

Subset

By definition of span, we want to know if there are scalars x1…

Theorem 1: The subspace spanned by a non-empty subset S of a v…

The set of all linear combinations of the vectors.... or ... The s…

A subset is a set of vectors. Assume a subset V∈ℜn... Can be a s…

Solving if something is in a Span

By definition of span, we want to know if there are scalars x1…

Span Theorems

Theorem 1: The subspace spanned by a non-empty subset S of a v…

System of Two Linear Equations

Solution

Consistent System

Inconsistent Solution

Consists of two equations that can be written as:... Ax + By = C…

An ordered pair (x,y) that satisfies each equation in the syst…

A system that has at least one solution.

A system that has no solutions.

System of Two Linear Equations

Consists of two equations that can be written as:... Ax + By = C…

Solution

An ordered pair (x,y) that satisfies each equation in the syst…

Use substitution! (2, 3) is (x, y)... y +…

x + y = 3 ---> (-1) + 4 = 3... 3 = 3 (tru…

The solution is: (2, 3)

The solution is (3, 0)

Is the point (2,3) a solution to the system below:... y + 4x = 1…

Is (-1, 4) a solution to the system below:... x + y = 3... 3x - 2y…

What is the solution to the following linear system?

What is the solution to the following linear system?

Use substitution! (2, 3) is (x, y)... y +…

Is the point (2,3) a solution to the system below:... y + 4x = 1…

x + y = 3 ---> (-1) + 4 = 3... 3 = 3 (tru…

Is (-1, 4) a solution to the system below:... x + y = 3... 3x - 2y…

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…

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…

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…

coordinate plane

origin

x-axis

y-axis

the grid created by the horizontal x-axis and the vertical y-a…

(0,0) in the coordinate plane; center of the grid

the horizontal number line in the coordinate plane (left to ri…

the vertical number line in the coordinate plane (up and down)

coordinate plane

the grid created by the horizontal x-axis and the vertical y-a…

origin

(0,0) in the coordinate plane; center of the grid