# Study sets matching "linear algebra relations"

Study sets

Diagrams

Classes

Users

analytic geometry

boundary

composite

composition

prove a theorem from plane geometry by placing the figure in a…

if an inequality is <= or >= the ________ is drawn a solid lin…

the new function created by mapping one set onto another

combining two functions

analytic geometry

prove a theorem from plane geometry by placing the figure in a…

boundary

if an inequality is <= or >= the ________ is drawn a solid lin…

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

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)

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…

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

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.

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…

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…

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,…Vector Space First Axiom

Vector Space Second Axiom

Vector Space Third Axiom

Vector Space Fourth Axiom

for all x,y under the set of V, x+y=y+x

for all x,y,z under the set of V, (x+y)+z=x+(y+z)

A zero vector exists in V, for all x in the set of V, x+(the z…

for all x under the set of V, the exists y under the set of V…

Vector Space First Axiom

for all x,y under the set of V, x+y=y+x

Vector Space Second Axiom

for all x,y,z under the set of V, (x+y)+z=x+(y+z)

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).

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…

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. (Height = H…

Mathematical

Having to do with numbers.

Variable

Something that can change like the height of a plant..

homogeneous linear equation

trivial solution to homogeneous

nontrivial solution to homogeneous

if zero vector is only solution

Ax = 0

vector x = 0... Span{0}

nonzero vector x that satisfies Ax = 0... can only exist IFF the…

solution set is Span{0}

homogeneous linear equation

Ax = 0

trivial solution to homogeneous

vector x = 0... Span{0}

cartesian plane

coordinates

origin

linear relation

a plane divided into four quadrants by the intersection of the…

Ordered pairs that identify points on a coordinate plane. (x,y)

(0,0) The point of intersection of the x-axis and y-axis in a…

A type of relationship that exists between two variables (usua…

cartesian plane

a plane divided into four quadrants by the intersection of the…

coordinates

Ordered pairs that identify points on a coordinate plane. (x,y)

There are only three types of solutions…

A system of linear equations is...

A system is called homogeneous if...

A system is called consistent if..

1. no solution. (parallel, no intersection, same slope)... 2. on…

is a list of linear equations in the same variables.

if each equation in the system is equal to zero. ... These system…

if there exists at least one solution. ... -a unique solution, wh…

There are only three types of solutions…

1. no solution. (parallel, no intersection, same slope)... 2. on…

A system of linear equations is...

is a list of linear equations in the same variables.

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