#### Study sets matching "linear algebra relations"

#### Study sets matching "linear algebra relations"

discrete relation

continuous relation

vertical line test

independent variable

domain is a set of individual points

domain of relation has an infinite number of elements and the…

can be used to determine whether it's a function

the variable, often x, with values making up the domain

discrete relation

domain is a set of individual points

continuous relation

domain of relation has an infinite number of elements and the…

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…

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…

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…

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,…Suppose we have a final solution set of…

How are two linear systems equivalent?

How do you solve a linear system?

A matrix with size 3x4 is: ____________…

infinite

They share the same solution sets

Replace the l.s. with one that is equivalent but "simpler", th…

augumented matrix of *

Suppose we have a final solution set of…

infinite

How are two linear systems equivalent?

They share the same solution sets

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.

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

consistent system

inconsistent system

leading entry

An equation that can be written as a1x1 + a2x2 + ... = b; a1,…

Has one or infinitely many solutions

Has no solution

Leftmost non-zero entry in a non-zero row

linear equation

An equation that can be written as a1x1 + a2x2 + ... = b; a1,…

consistent system

Has one or infinitely many solutions

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,…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

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..

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

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)

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…

cartesian plane

coordinates

quadrants

origin

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

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

Four regions into which a coordinate plane is divided by the x…

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

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)

find the y intercept, slope. y=2x+3

will the slope be + or - y=-4x-9

will the slope be + or - y=-5

you are about to go trick or treating.…

m=2, b=3

negative

zero

x= 77

find the y intercept, slope. y=2x+3

m=2, b=3

will the slope be + or - y=-4x-9

negative

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).

Matix

Elements of the matrix

Submatrix

Square matrix

A rectangular array of numbers.

The numbers in the array

A matrix composed of a array of numbers taken from a larger ma…

When there are equal numbers of rows as Columns

Matix

A rectangular array of numbers.

Elements of the matrix

The numbers in the array

Linear combination

Linearly independent

Theorem 5.1.1

elementary vectors

an expression of the form c1v1+c2v2+...+cnvn where all the ci…

a set of vectors in LI if the only way to write the zero vecto…

A set of vectors is LD iff one of the vectors can be written a…

vectors that have exactly one component equal to 1 and all oth…

Linear combination

an expression of the form c1v1+c2v2+...+cnvn where all the ci…

Linearly independent

a set of vectors in LI if the only way to write the zero vecto…

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…