# 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

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Interval Notation

Set Builder Notation

Disjunction

Conjunction

shows the endpoints of a solution set

two simple inequalities joined by the word OR

a compound inequality joined by the word AND

Interval Notation

shows the endpoints of a solution set

Set Builder Notation

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.

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,…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…

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

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)

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

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…

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.

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…

Algebraically, the value of the output when the input is zero…

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…

Absolute Value

Integer

Exponent

Function

a number's distance from zero

positive and negative whole numbers

tells how many times to multiply the base number

a relationship where the input determines the output

Absolute Value

a number's distance from zero

Integer

positive and negative whole numbers

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…

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…

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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)…

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

If the augmented matrices of 2 linear s…

Another way to ask if a system is consi…

Echelon Form (properties)

Reduced Echelon Form (properties)

the 2 have the same solution set

does at least 1 solution exist

All non zero rows above zero rows... each leading entry of a row…

All properties from Echelon Form... leading entry is 1 in each n…

If the augmented matrices of 2 linear s…

the 2 have the same solution set

Another way to ask if a system is consi…

does at least 1 solution exist

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…