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Study sets matching "linear algebra relations"

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Study sets matching "linear algebra relations"

50 terms
Algebra: Linear Relations and Functions
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…
24 terms
Algebra I - Linear Relations and Functions
analytic geometry
boundary
composite
composition
prove a theorem from plane geometry by placing the figure in…
if an inequality is <= or >= the ________ is drawn a solid li…
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…
boundary
if an inequality is <= or >= the ________ is drawn a solid li…
25 terms
Algebra Test- Linear Relations Vocab
correlation
(quantitative) bi-variate data
causation
negative correlation
description of the linear relationship between the 2 variable…
data for TWO related variables that can represented by a scat…
a relationship between two variables in which one variable di…
trend descends L to R
correlation
description of the linear relationship between the 2 variable…
(quantitative) bi-variate data
data for TWO related variables that can represented by a scat…
19 terms
Algebra II Chapter 2 Linear Relations and Functions Vocabulary
one-to-one function
onto function
discrete relation
continuous relation
A function where each element of the range is paired with exa…
Each element of the range corresponds to an element of the do…
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 exa…
onto function
Each element of the range corresponds to an element of the do…
15 terms
**Linear Relations
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…
Mathematical
Having to do with numbers.
Variable
Something that can change like the height of a plant.
19 terms
***Linear Relations
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 he…
Mathematical
Having to do with numbers.
Variable
Something that can change like the height of plant.
126 terms
Linear Algebra
Reduced row echelon form conditions
Theorem "dimension characterizes isomo…
Define "W is isomorphic to V"
Theorem stating "isomorphic to" is an…
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 iso…
There exists an isomorphism T:W->V
"isomorphic to" is an equivalence relation for subspaces V wi…
Reduced row echelon form conditions
1. leading entry (if there is one) is 1 2. if column contains…
Theorem "dimension characterizes isomo…
For subspaces V within R^n and W within R^m, we have V is iso…
66 terms
Linear Algebra
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 en, [1, 0, 0, 0...0] to the nth number. So in R3…
Two vectors, when added together, are still in the same subsp…
When a vector is multiplied by a scalar, it's still in the sa…
Scalar multiplication
Multiplication of vectors by t, such that it becomes t(v1), t…
Standard Basis in Rn
Denoted by en, [1, 0, 0, 0...0] to the nth number. So in R3…
15 terms
Linear Algebra
Slope Intercept Form
System of linear equations
Point Slope Form
The answer to a system of linear equat…
y= mx + b
2x + y = 5 ... 3x - y = 6
y - y^1 = m(x - x^1)
Ordered Pair
Slope Intercept Form
y= mx + b
System of linear equations
2x + y = 5 ... 3x - y = 6
126 terms
Linear Algebra
Reduced row echelon form conditions
Theorem "dimension characterizes isomo…
Define "W is isomorphic to V"
Theorem stating "isomorphic to" is an…
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 iso…
There exists an isomorphism T:W->V
"isomorphic to" is an equivalence relation for subspaces V wi…
Reduced row echelon form conditions
1. leading entry (if there is one) is 1 2. if column contains…
Theorem "dimension characterizes isomo…
For subspaces V within R^n and W within R^m, we have V is iso…
66 terms
Linear Algebra
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 en, [1, 0, 0, 0...0] to the nth number. So in R3…
Two vectors, when added together, are still in the same subsp…
When a vector is multiplied by a scalar, it's still in the sa…
Scalar multiplication
Multiplication of vectors by t, such that it becomes t(v1), t…
Standard Basis in Rn
Denoted by en, [1, 0, 0, 0...0] to the nth number. So in R3…
67 terms
Linear algebra
What is a subspace and what are the re…
Column Space?
What is closure?
What is true for the span of a set of…
A subset (H) of a larger set of vectors(V) that has 3 propert…
denoted col(A)... the span of the columns of A.
When an operation such as addition is done with two numbers f…
For a set of vectors {v₁, v₂, v₃....} in Rⁿ... span{v₁,v₂,v₃...…
What is a subspace and what are the re…
A subset (H) of a larger set of vectors(V) that has 3 propert…
Column Space?
denoted col(A)... the span of the columns of A.
10 terms
*Linear Relations
Variable
Mathematical Variable
Linear
Rise
Something that can change like the height of plant.
Numbers that can change; symbolized with a letter. Example he…
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 he…
22 terms
Linear Relations
cartesian plane
coordinates
quadrants
origin
a plane divided into four quadrants by the intersection of th…
Ordered pairs that identify points on a coordinate plane. (x,y)
Four regions into which a coordinate plane is divided by the…
(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 th…
coordinates
Ordered pairs that identify points on a coordinate plane. (x,y)
10 terms
*Linear Relations
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 =…
Mathematical
Having to do with numbers.
Variable
Something that can change like the height of a plant..
15 terms
**Linear Relations
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 he…
Relation that graphs a straight line.
Variable
Something that can change like the height of plant.
Constant Rate
Stay at the same speed
67 terms
Linear algebra
What is a subspace and what are the re…
Column Space?
What is closure?
What is true for the span of a set of…
A subset (H) of a larger set of vectors(V) that has 3 propert…
denoted col(A)... the span of the columns of A.
When an operation such as addition is done with two numbers f…
For a set of vectors {v₁, v₂, v₃....} in Rⁿ... span{v₁,v₂,v₃...…
What is a subspace and what are the re…
A subset (H) of a larger set of vectors(V) that has 3 propert…
Column Space?
denoted col(A)... the span of the columns of A.
67 terms
Linear algebra
What is a subspace and what are the re…
Column Space?
What is closure?
What is true for the span of a set of…
A subset (H) of a larger set of vectors(V) that has 3 propert…
denoted col(A)... the span of the columns of A.
When an operation such as addition is done with two numbers f…
For a set of vectors {v₁, v₂, v₃....} in Rⁿ... span{v₁,v₂,v₃...…
What is a subspace and what are the re…
A subset (H) of a larger set of vectors(V) that has 3 propert…
Column Space?
denoted col(A)... the span of the columns of A.
17 terms
Linear Relations
cartesian plane
coordinates
origin
linear relation
a plane divided into four quadrants by the intersection of th…
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 (usu…
cartesian plane
a plane divided into four quadrants by the intersection of th…
coordinates
Ordered pairs that identify points on a coordinate plane. (x,y)
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
34 terms
Linear Algebra
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
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
92 terms
linear algebra
matrix notation for an entry
augmented matrix
row-echelon form
Gaussian elimination
(A)ij means the entry for A in the i row and the j column. Or…
where you have the solutions set up as another column; the ri…
Any rows entirely of 0 are at the bottom. Each row's first no…
*I think* where you do row operations starting at the top and…
matrix notation for an entry
(A)ij means the entry for A in the i row and the j column. Or…
augmented matrix
where you have the solutions set up as another column; the ri…
10 terms
Linear and Non-Linear Relations
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).
9 terms
Algebra Linear functions
Y- intercept
Slope
Slope- intercept Form
Point- slope form
the y-coordinate of a point where a graph crosses the y-axis
the steepness of a line on a graph, equal to its vertical cha…
an equation written in the form y=mx+b is in slope-intercept…
y-y1 = m(x-x1), where m is the slope and (x1,y1) is the point…
Y- intercept
the y-coordinate of a point where a graph crosses the y-axis
Slope
the steepness of a line on a graph, equal to its vertical cha…
66 terms
Linear Algebra
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 en, [1, 0, 0, 0...0] to the nth number. So in R3…
Two vectors, when added together, are still in the same subsp…
When a vector is multiplied by a scalar, it's still in the sa…
Scalar multiplication
Multiplication of vectors by t, such that it becomes t(v1), t…
Standard Basis in Rn
Denoted by en, [1, 0, 0, 0...0] to the nth number. So in R3…
100 terms
Linear Algebra
linear equation
system of linear equations
solution set
equivalent linear systems
an equation that can be written in the form a1x1 + a2x2 + ...…
a collection of one or more linear equations involving the sa…
a list of numbers that makes each equation in a system a true…
linear systems with the same solution set
linear equation
an equation that can be written in the form a1x1 + a2x2 + ...…
system of linear equations
a collection of one or more linear equations involving the sa…
18 terms
Linear Relations
Variable
Isolate The Variable
Solution
Greater Than
A symbol used to represent a quantity that can change
To get a variable alone on one side of an equation or inequal…
The set containing values of the variables
Used to compare two numbers when the first number is larger t…
Variable
A symbol used to represent a quantity that can change
Isolate The Variable
To get a variable alone on one side of an equation or inequal…
20 terms
Linear Relations
When factorising
Inverse
To solve linear equations
Cross multiplying
Take out the number in brackets
When you multiply something by its inverse you get one
Work backwards with inverse operations
Only when its equal two fraction... Basically lift and swap the…
When factorising
Take out the number in brackets
Inverse
When you multiply something by its inverse you get one
42 terms
Linear Algebra
Elementary Row Operations
Row Equivalency
Two equivalent equivalent augmented ma…
Two Fundamental Questions
1. Replacement... 2. Scaling... 3. Interchange
A is row equivalent to B if we can get from A to B via a sequ…
solution set
1. Is the system consistent... 2. If the solution exists, is the…
Elementary Row Operations
1. Replacement... 2. Scaling... 3. Interchange
Row Equivalency
A is row equivalent to B if we can get from A to B via a sequ…
Linear Algebra Chapter 1
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 r…
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
51 terms
Linear Algebra
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 vect…
A set of vectors is LD iff one of the vectors can be written…
vectors that have exactly one component equal to 1 and all ot…
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 vect…
97 terms
Linear algebra
Definition of a vector space
8 axioms of a vector space
Notation for a vector space with n dim…
Definition of a linear combination of…
V (set of elements: x, y, u, v) is called a vector space of K…
1) *u, v, w* ∈ V, (*u* + *v*) + *w* = *u* + (*v* + *w*) (Asso…
ℝⁿ
*x* is a linear combination of *v₁, ... vₙ* if for *v₁, ... v…
Definition of a vector space
V (set of elements: x, y, u, v) is called a vector space of K…
8 axioms of a vector space
1) *u, v, w* ∈ V, (*u* + *v*) + *w* = *u* + (*v* + *w*) (Asso…
32 terms
Linear Algebra Test 1
Vector Space
Vector Space Axioms
Subspace
Transpose
a set where addition and scalar multiplication as well as the…
1. Commutativity of addition... 2. Associativity in addition... 3.…
a subset of a vector space that is also a vector space closed…
Matrix formed from switching rows and colums (A₁₂)'=A₂₁
Vector Space
a set where addition and scalar multiplication as well as the…
Vector Space Axioms
1. Commutativity of addition... 2. Associativity in addition... 3.…
42 terms
Linear Algebra
Solution of an SLE
Consistent SLE
Inconsistent SLE
Equivalent linear system
A SLE has (1) no solution, or (2) exactly one solution, or (3…
SLE has one or infinitely many solutions.
SLE has no solution.
A SLE that have the same solution set
Solution of an SLE
A SLE has (1) no solution, or (2) exactly one solution, or (3…
Consistent SLE
SLE has one or infinitely many solutions.
15 terms
Linear Algebra
Elementary Matrix
property of Elementary Matrix
Cramer's Rule2
subspace of Rn
what an n x n matrix E is called if we can obtain E from I, b…
each of these elementary row operations can be implemented by…
(a) the sum of any pair of vectors in the set lies in the set…
Elementary Matrix
what an n x n matrix E is called if we can obtain E from I, b…
property of Elementary Matrix
each of these elementary row operations can be implemented by…
65 terms
Linear Algebra
Solving if something is in a Span
Span Theorems
Span
Subset
By definition of span, we want to know if there are scalars x…
Theorem 1: The subspace spanned by a non-empty subset S of a…
The set of all linear combinations of the vectors.... or ... The…
A subset is a set of vectors. Assume a subset V∈ℜn... Can be a…
Solving if something is in a Span
By definition of span, we want to know if there are scalars x…
Span Theorems
Theorem 1: The subspace spanned by a non-empty subset S of a…
10 terms
Linear Algebra
the image of at least one x ∈ R.
T(u + v) = T(u) + T(v)
T(cu) = cT(u)
row equivalent
A transformation T : Rn → Rm is one-to-one if each b ∈ Rm is…
_________ for all u, v in the domain of T.
_________ for all scalars c and all vectors u in the domain o…
two matrices are _________ if one can be changed to the other…
the image of at least one x ∈ R.
A transformation T : Rn → Rm is one-to-one if each b ∈ Rm is…
T(u + v) = T(u) + T(v)
_________ for all u, v in the domain of T.
12 terms
Linear Relations
The slope of a line
The point where x=0
Half way between 2 points
Gradient
Gradient
y intercept
mid point
rise/run
The slope of a line
Gradient
The point where x=0
y intercept
19 terms
Linear Algebra
Col A
Nul A
Rank
Col A(T)
Pivot Columns
Free variables in parametric form
number of pivot columns
Pivot Row
Col A
Pivot Columns
Nul A
Free variables in parametric form
34 terms
linear algebra
3.1 Two equivalent vectors must have t…
3.1 The vectors (a,b) and (a,b,0) are…
3.1 If k is a scalar and v is a vector…
3.1 The vectors v+(u+w) and (w+v)+u ar…
F (옮겨서 시점이 달라져도 같은 벡터로 취급한다.)
F (일단 기본적으로 차원이 같아야 함.)
F (벡터가 평행하다는 것은 굳이 방향이 같을 필요는 없음. 방향은 반대더라도 됨.)
T
3.1 Two equivalent vectors must have t…
F (옮겨서 시점이 달라져도 같은 벡터로 취급한다.)
3.1 The vectors (a,b) and (a,b,0) are…
F (일단 기본적으로 차원이 같아야 함.)
16 terms
Linear algebra
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 m…
When there are equal numbers of rows as Columns
Matix
A rectangular array of numbers.
Elements of the matrix
The numbers in the array
6 terms
Linear Algebra
Truculent
Rapacious
Misanthrope
Craven
Eager or quick to argue or fight; aggressively defiant. ... Syn:…
Person who is abnormally anxious about their health.... Syn: Val…
General hatred, distrust and contempt of the human species or…
A cowardly person; contemptibly lacking in courage. "A craven…
Truculent
Eager or quick to argue or fight; aggressively defiant. ... Syn:…
Rapacious
Person who is abnormally anxious about their health.... Syn: Val…
80 terms
Linear Algebra
Linear Equation
System of Linear Equations
Solution
Solution Set
A LINEAR EQUATION in variables x₁,x₂,....,xⁿ (for n a positiv…
A SYSTEM OF LINEAR EQUATIONS is a collection of one or more l…
A SOLUTION to a linear system is a list (s₁,s₂,...,sⁿ) of num…
The set of all solutions to a linear system is called the SOL…
Linear Equation
A LINEAR EQUATION in variables x₁,x₂,....,xⁿ (for n a positiv…
System of Linear Equations
A SYSTEM OF LINEAR EQUATIONS is a collection of one or more l…
128 terms
Linear algebra
What is a subspace and what are the re…
Column Space?
column rank
Row space
A subset (H) of a larger set of vectors(V) that has 3 propert…
denoted col(A)... the span of the columns of A.... the basis are th…
cr:=dim(column space)
denoted row(A)... the span of rows of A... the basis is all nonzero…
What is a subspace and what are the re…
A subset (H) of a larger set of vectors(V) that has 3 propert…
Column Space?
denoted col(A)... the span of the columns of A.... the basis are th…
Linear Algebra
Suppose we have a final solution set o…
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", t…
augumented matrix of *
Suppose we have a final solution set o…
infinite
How are two linear systems equivalent?
They share the same solution sets
13 terms
Linear Algebra
A finite basis for V of Field F is a f…
Let S be a nonempty subset of a vector…
Let V & W be vector spaces over field…
A nonempty finite subset {u1, u2,.....…
Finite Basis
Span
Linear Transformations (Operators)
Linear Dependent
A finite basis for V of Field F is a f…
Finite Basis
Let S be a nonempty subset of a vector…
Span
108 terms
Friedell Linear Algebra Vocabulary
Order of Operations
Inequality
Like Terms
Equivalent expressions
Ch. 1 PEMDAS the order in which you solve an equation. (Paren…
Ch. 1 An open sentence that contains the symbols < >
Ch. 1 Terms that contain the same variables, with correspondi…
Ch. 1 Expressions that simplify to the same number.
Order of Operations
Ch. 1 PEMDAS the order in which you solve an equation. (Paren…
Inequality
Ch. 1 An open sentence that contains the symbols < >
24 terms
Linear Algebra
What is the null space of matrix A? Wh…
A subspace of Rⁿ is any set H in Rⁿ th…
What is the column space of matrix A?
The set {e₁; ...; eη} is called the __…
The null space of a matrix A is the set Nul A of all solution…
a. The zero vector is in H.... b. For each u and v in H, the sum…
The column space of a matrix A is the set Col A of all linear…
standard basis
What is the null space of matrix A? Wh…
The null space of a matrix A is the set Nul A of all solution…
A subspace of Rⁿ is any set H in Rⁿ th…
a. The zero vector is in H.... b. For each u and v in H, the sum…
14 terms
Linear Algebra
What is a vector?
What is a matrix?
What is the vector space?
What are the 8 axioms of vector space?
Vector: a quantity with more than one element (more than one…
Put simply, a rectangular array of numbers, symbols, expressi…
A vector space (also called a linear space) is a collection o…
What is a vector?
Vector: a quantity with more than one element (more than one…
What is a matrix?
Put simply, a rectangular array of numbers, symbols, expressi…
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