# Study sets matching "linear algebra relations"

Study sets

Diagrams

Classes

Users

ordered pair

Cartesian coordinate

plane

quadrant

A pair of numbers used to locate a point on a coordinate plane…

is composed of the x-axis (horizontal) and the y-axis (vertica…

A two-dimensional flat surface that extends in all directions

one of four sections into which the coordinate plane is divided

ordered pair

A pair of numbers used to locate a point on a coordinate plane…

Cartesian coordinate

is composed of the x-axis (horizontal) and the y-axis (vertica…

y-intercept

X-intercept

Standard form

Linear relation

Point at which graph crosses y-axis

Point at which graph crosses x-axis

Linear equation written in the form Ax+By=C,where A,B,C are in…

Forms straight line graph

y-intercept

Point at which graph crosses y-axis

X-intercept

Point at which graph crosses x-axis

one-to-one function

onto function

discrete relation

continuous relation

A function where each element of the range is paired with exac…

Each element of the range corresponds to an element of the dom…

A relation in which the domain is a set of individual points.

A relation that can be graphed with a line or smooth curve.

one-to-one function

A function where each element of the range is paired with exac…

onto function

Each element of the range corresponds to an element of the dom…

Mathematical

Variable

Constant Rate

Mathematical Variable

Having to do with numbers.

Something that can change like the height of a plant.

Stay at the same speed

Numbers that can change; symbolized with a letter. Example h e…

Mathematical

Having to do with numbers.

Variable

Something that can change like the height of a plant.

Variable

Constant Rate

Mathematical Variable

Linear

Something that can change like the height of plant.

Stay at the same speed

Numbers that can change; symbolized with a letter. Example hei…

Relation that graphs a straight line.

Variable

Something that can change like the height of plant.

Constant Rate

Stay at the same speed

correlation

(quantitative) bi-variate data

causation

negative correlation

description of the linear relationship between the 2 variables…

data for TWO related variables that can represented by a scatt…

a relationship between two variables in which one variable dir…

trend descends L to R

correlation

description of the linear relationship between the 2 variables…

(quantitative) bi-variate data

data for TWO related variables that can represented by a scatt…

Relation

Domain

Range

Function

Set of order pairs... (x,y)

The set of x-values ... (Input,Independant Variable)

Set of y-values ... (Output,dependant)

Relation in which x DOES NOT REPEAT

Relation

Set of order pairs... (x,y)

Domain

The set of x-values ... (Input,Independant Variable)

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

Mathematical

Variable

Constant Rate

Mathematical Variable

Having to do with numbers.

Something that can change like the height of plant.

Stay at the same speed

Numbers that can change; symbolized with a letter. Example hei…

Mathematical

Having to do with numbers.

Variable

Something that can change like the height of plant.

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

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…

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…

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,…linear equation

slope

Types of Slope

y-intercept

An equation in two variables whose graph in a coordinate plane…

A ratio comparing the change in output over the change in inpu…

The value of the output when the input is zero (0, y). The poi…

linear equation

An equation in two variables whose graph in a coordinate plane…

slope

A ratio comparing the change in output over the change in inpu…

Reduced row echelon form conditions

Theorem "dimension characterizes isomor…

Define "W is isomorphic to V"

Theorem stating "isomorphic to" is an e…

1. leading entry (if there is one) is 1 2. if column contains…

For subspaces V within R^n and W within R^m, we have V is isom…

There exists an isomorphism T:W->V

"isomorphic to" is an equivalence relation for subspaces V wit…

Reduced row echelon form conditions

1. leading entry (if there is one) is 1 2. if column contains…

Theorem "dimension characterizes isomor…

For subspaces V within R^n and W within R^m, we have V is isom…

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

linear equation

slope

y-intercept

x-intercept

An equation in two variables whose graph in a coordinate plane…

A ratio comparing the change in output over the change in inpu…

The value of the output when the input is zero (0, y). The poi…

The value of the input when the output is zero (x, 0). The poi…

linear equation

An equation in two variables whose graph in a coordinate plane…

slope

A ratio comparing the change in output over the change in inpu…

Vector Space

Vector Space Axioms

Subspace

Linear Combination

A nonempty set V of vectors following 10 axioms for vectors u,…

1: u + v is in V... 2: u + v = v + u... 3: (u + v) + w = u + (v + w)…

A subspace H of vector space V is a subset that has three prop…

Any sum of scalar multiples of vectors

Vector Space

A nonempty set V of vectors following 10 axioms for vectors u,…

Vector Space Axioms

1: u + v is in V... 2: u + v = v + u... 3: (u + v) + w = u + (v + w)…

Linear Equation

System of Linear Equations

Solution

Solution Set

describes a firsrt order line in Rn equations of the form a1x1…

collection of 1+ linear equations to be solved simultaneously

a set of real numbers s1...sn such that each equation holds if…

a set of all solutions in a system

Linear Equation

describes a firsrt order line in Rn equations of the form a1x1…

System of Linear Equations

collection of 1+ linear equations to be solved simultaneously

Direct Variation

Partial Variation

y = kx

y = kx + b

A line on a graph that goes through the origin (0,0).

A line on a graph that does not go through the origin (0,0).

The equation of a direct variation.

The equation of a partial variation.

Direct Variation

A line on a graph that goes through the origin (0,0).

Partial Variation

A line on a graph that does not go through the origin (0,0).

Mathematical

Variable

Constant Rate

Mathematical Variable

Having to do with numbers.

Something that can change like the height of a plant.

Stay at the same speed

Numbers that can change; symbolized with a letter. Example h e…

Mathematical

Having to do with numbers.

Variable

Something that can change like the height of a plant.

12.50

25

11

100

Jesus brought $20 to the game. He is fond of blow pops, which…

Elicia currently has $250 in savings. She wants to make money…

Brian raises Black Angus cattle. He starts with a herd of 35,…

Sierra has 1000 Pokemon cards that she wants to get rid of. Sh…

12.50

Jesus brought $20 to the game. He is fond of blow pops, which…

25

Elicia currently has $250 in savings. She wants to make money…

Variable

Mathematical Variable

Linear

Rise

Something that can change like the height of plant.

Numbers that can change; symbolized with a letter. Example hei…

Relation that graphs a straight line.

How far "up" you go. Vertical Height

Variable

Something that can change like the height of plant.

Mathematical Variable

Numbers that can change; symbolized with a letter. Example hei…