# 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…

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…

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…

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,…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

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…

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…

Free Variable Theorem for Homogeneous s…

a homo geneous linear system with more…

If B and C are both inverses of the mat…

If A and B are invertible matrices with…

If a homogeneous linear system has n unknowns, and if the redu…

infinitley many solutions

since B is an inverse of A, we have BA=I. Multiplying both sid…

(AB)(B^-1A^-1)=(B^-1A^-1)(AB)=I , but ... (AB)(B^-1A^-1)=A(BB^-1)…

Free Variable Theorem for Homogeneous s…

If a homogeneous linear system has n unknowns, and if the redu…

a homo geneous linear system with more…

infinitley 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…

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

-6

10

-1

3

Find the y-coordinate using elimination method: ... -4x - 2y = -1…

Find the x-coordinate using elimination method... x - y = 11... 2x +…

Find the y-coordinate using elimination method ... -6x + 5y = 1... 6…

Find the y-coordinate using elimination method... -2x - 9y = -25…

-6

Find the y-coordinate using elimination method: ... -4x - 2y = -1…

10

Find the x-coordinate using elimination method... x - y = 11... 2x +…

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…

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

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…

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

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…