Study sets matching "i linear algebra"

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Study sets matching "i linear algebra"

21 terms
Linear Functions (Algebra 1)
linear equation
slope
y-intercept
x-intercept
An equation in two variables whose graph in a coordinate plan…
A ratio comparing the change in output over the change in inp…
The value of the output when the input is zero (0, y). The po…
The value of the input when the output is zero (x, 0). The po…
linear equation
An equation in two variables whose graph in a coordinate plan…
slope
A ratio comparing the change in output over the change in inp…
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
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
17 terms
Algebra 1: Linear Vocabulary
Quadrant
Solution of an equation in two variables
Graph of an equation in two variables
Linear equation
One of the four regions into which the x and y axes divide th…
An ordered pair that produces a true statement when the coord…
The set of points in a coordinate plane that represent all so…
An equation whose graph is a line.
Quadrant
One of the four regions into which the x and y axes divide th…
Solution of an equation in two variables
An ordered pair that produces a true statement when the coord…
Linear Algebra Exam 1
Equivalent Systems
consistent system
inconsistent system
Row Echelon Form Qualifications [REF]…
Have the same solution set
either one solution or infinitely many
no solution
1. All zero rows below nonzero rows... 2. Each leading entry of…
Equivalent Systems
Have the same solution set
consistent system
either one solution or infinitely many
104 terms
Linear Algebra Chapter 1
Linear Equation
Coefficients
System of Linear Equations/Linear System
Solution
a1x1 + a2x2 +... + anxn=b
a1...an are real or complex numbers.
A collection of one or more linear equations involving the sa…
A list of numbers that makes each equation a true statement w…
Linear Equation
a1x1 + a2x2 +... + anxn=b
Coefficients
a1...an are real or complex numbers.
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.…
5 terms
Linear Algebra 1.4
Matrix equation
Theorem 3
Identity matrix
Theorem 4
an equation that involves at least one matrix for instance, A…
If A is an m*n matrix, with columns a1...an, and if b is in R…
A square matrix with ones on the diagonal and zeros elsewhere
Let A be an m*n matrix. Then the following statements are log…
Matrix equation
an equation that involves at least one matrix for instance, A…
Theorem 3
If A is an m*n matrix, with columns a1...an, and if b is in R…
18 terms
Linear Algebra Test 1
basic variable
existance
consistent
inconsistant
variable that corresponds to a pivot column in the coefficien…
there is at least one solution to the matrix
the system of equations has at least one solution
the system has no solutions
basic variable
variable that corresponds to a pivot column in the coefficien…
existance
there is at least one solution to the matrix
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
Algebra 1: Linear Functions
Slope
Y-intercept
Standard Form
Slope-intercept Form
(y₂-y₁)/(x₂-x₁)
The point where the graph crosses the y-axis. In a linear equ…
Ax + By=C, where A, B, and C are not decimals or fractions, w…
y=mx+b, where m is the slope and b is the y-intercept of the…
Slope
(y₂-y₁)/(x₂-x₁)
Y-intercept
The point where the graph crosses the y-axis. In a linear equ…
31 terms
Algebra 1 Linear Review
D
A
D
B
D
A
21 terms
Algebra 1 Linear Equations
D
A
D
B
D
A
14 terms
Algebra 1: Linear Equations
Rate of change
Slope
The Slope Formula
Positive Slope
Rate of change
Slope
31 terms
Algebra 1: Linear Review
D
A
D
B
D
A
6 terms
Linear algebra 1.1
solution
Gauss-Jordan elimination
elementary transformations
Echelon system
pair of x and y values that satisfies all equations in a syst…
1) put in augmented matrix form... 2) make triangle of zeros on…
interchanging equations, multiplying a row by a nonzero const…
3 zeros in the lower left hand corner
solution
pair of x and y values that satisfies all equations in a syst…
Gauss-Jordan elimination
1) put in augmented matrix form... 2) make triangle of zeros on…
Algebra 1- Linear Functions
X-Intercept
Y-Intercept
Linear Function
Rate
The x-coordinate(s) of the point(s) where a graph intersects…
The y-coordinate(s) of the point(s) where a graph intersects…
A function that can be written in the form y=mx+b, where x is…
A ratio that compares two quantities measured in different un…
X-Intercept
The x-coordinate(s) of the point(s) where a graph intersects…
Y-Intercept
The y-coordinate(s) of the point(s) where a graph intersects…
25 terms
Linear Functions (Algebra 1)
linear equation
slope
y-intercept
x-intercept
An equation in two variables whose graph in a coordinate plan…
A ratio comparing the change in output over the change in inp…
The value of the output when the input is zero (0, y). The po…
The value of the input when the output is zero (x, 0). The po…
linear equation
An equation in two variables whose graph in a coordinate plan…
slope
A ratio comparing the change in output over the change in inp…
Algebra 1: Linear Equations
coordinate plane
origin
x-axis
y-axis
the grid created by the horizontal x-axis and the vertical y-…
(0,0) in the coordinate plane; center of the grid
the horizontal number line in the coordinate plane (left to r…
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-…
origin
(0,0) in the coordinate plane; center of the grid
20 terms
Algebra 1: Vocabulary (Linear, Slope)
rate or rate of change
constant rate of change
constant rate of change
zero rate
measure like miles per hour or price per item
rate that stays the same throughout the table
graph of this rate is a straight line
graph of this rate is a horizontal line
rate or rate of change
measure like miles per hour or price per item
constant rate of change
rate that stays the same throughout the table
Linear Algebra 1:1
Linear Equation
Linear Coefficients
System of linear equations (linear sys…
Solution of a linear system
1. variables x1......xn that can be written in the form:... a1x1…
Can be real or complex numbers
Collection of one of more linear equations that contain x1...…
List (s1, s2.....,sn) of numbers that makes each equation a t…
Linear Equation
1. variables x1......xn that can be written in the form:... a1x1…
Linear Coefficients
Can be real or complex numbers
Linear Algebra 1:2
The leading entry of the row is the:
Echelon Matrix Form
Reduced Echelon Matrix Form
Inconsistent/Consistent Matrices and E…
leftmost nonzero entry in that row
1. All nonzero rows are above any rows of zeros... 2. "Stairstep…
1. Same three reqs. as echelon form... 2. Leading entry is 1... 3.…
1. If there is a solution, there is a reduced echelon form to…
The leading entry of the row is the:
leftmost nonzero entry in that row
Echelon Matrix Form
1. All nonzero rows are above any rows of zeros... 2. "Stairstep…
Linear Algebra 1:5
Homogeneous Linear System
Trivial/Nontrivial Solutions
The homogeneous equation Ax=0 has a no…
A nontrivial solution x can have some…
1. A system of linear equations is said to be homogeneous if…
1. The zero solution is called the trivial solution... 2. The no…
the equation has at least one free variable.
not all of the entries are zero.
Homogeneous Linear System
1. A system of linear equations is said to be homogeneous if…
Trivial/Nontrivial Solutions
1. The zero solution is called the trivial solution... 2. The no…
Linear Algebra 1.1
Is the statement​ "Every elementary ro…
Is the statement​ "A 5×6 matrix has si…
Is the statement​ "Two fundamental que…
Is the statement​ "Two matrices are ro…
True, because​ replacement, interchanging, and scaling are al…
False, because a 5×6 matrix has five rows and six columns.
True, because two fundamental questions address whether the s…
False, because if two matrices are row equivalent it means th…
Is the statement​ "Every elementary ro…
True, because​ replacement, interchanging, and scaling are al…
Is the statement​ "A 5×6 matrix has si…
False, because a 5×6 matrix has five rows and six columns.
26 terms
2.1 Linear Algebra
(i,j)-entry of A
The diagonal entries of A
Main diagonal
Diagonal matrix
The entry in A in the ith row and the jth column.
a11, a22,a33...
The diagonal of A formed by the diagonal entries.
A square n x n matrix whose nondiagonal entries are zero.
(i,j)-entry of A
The entry in A in the ith row and the jth column.
The diagonal entries of A
a11, a22,a33...
29 terms
Linear Algebra Exam #1
1 parameter
2 parameters
3 parameters
mxn
line
plane
hyper-plane
m rows by n columns
1 parameter
line
2 parameters
plane
Linear Algebra 1.3
The number c in cu is a _________.
R^2 is a _______.
Vectors in R^3 are ______ X _______ co…
Vectors in R^3 are represented in ____…
scalar
rectangular coordinate system in a plane.
3; 1
three
The number c in cu is a _________.
scalar
R^2 is a _______.
rectangular coordinate system in a plane.
Linear Algebra 1:8
Transformation
Domain of T
Codomain of T
Image
A transformation T from R(n) -> R(m) is a rule that assigns t…
Set R(n)
Set R(m)
For x in R(n), the vector T(x) in R(m) is called the image of…
Transformation
A transformation T from R(n) -> R(m) is a rule that assigns t…
Domain of T
Set R(n)
10 terms
Algebra 1- Linear Equations
Standard Form
Slope Intercept Form
Vertical line
Horizontal line
ax+by=c
y=mx+b
x=a m=undefined
y=b m=0
Standard Form
ax+by=c
Slope Intercept Form
y=mx+b
Linear Algebra 1:7
Linearly independent
Linearly dependent
Linear Independence of Matrix Columns
Set of One Vector
1. Indexed set of vectors {v1,...vp} in R(n) is said to be li…
1. Indexed set of vectors {v1,...vp} in R(n) is said to be li…
The columns of a matrix A are linearly independent iff the eq…
1. A set of one vector is linearly independent iff v is NOT t…
Linearly independent
1. Indexed set of vectors {v1,...vp} in R(n) is said to be li…
Linearly dependent
1. Indexed set of vectors {v1,...vp} in R(n) is said to be li…
Linear Algebra 1:3
Vector
R^(n)
R2
Equal R2 vectors
An ordered list of members
-R stands for the real numbers that appear as entries in the…
The set of all vectors with two entries
Two vectors in R2 are equal iff their corresponding entries a…
Vector
An ordered list of members
R^(n)
-R stands for the real numbers that appear as entries in the…
Linear Algebra 1:4
Definition of Linear Combination
Matrix Equation
Theorem 3
Solution of Ax=b
1. If A is an m x n matrix, with columns a1, ... an, and if x…
Ax = b
1. If A is an m x n matrix with columns a1,...,an, and if b i…
1. The equation Ax=b has a solution iff b is a linear combina…
Definition of Linear Combination
1. If A is an m x n matrix, with columns a1, ... an, and if x…
Matrix Equation
Ax = b
66 terms
Linear Algebra Test 1
If the augmented matrices of 2 linear…
Another way to ask if a system is cons…
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 ro…
All properties from Echelon Form... leading entry is 1 in each…
If the augmented matrices of 2 linear…
the 2 have the same solution set
Another way to ask if a system is cons…
does at least 1 solution exist
15 terms
Linear Algebra Chapter 1
consistent linear system
inconsistent linear system
free variable
vector
a linear system with at least one solution
a linear system with no solution
any variable in a linear system that is not a basic variable
a list of numbers; a matrix with only one column
consistent linear system
a linear system with at least one solution
inconsistent linear system
a linear system with no solution
10 terms
Linear Algebra 1.7
Linearly independent and linearly depe…
Linear dependence relation
The columns of matrix A are linearly i…
A set containing only one vector is li…
the equation Ax = 0 has only the trivial solution.
that vector is not the zero vector.
Linearly independent and linearly depe…
Linear dependence relation
Algebra 1 Linear Equations
D
A
D
B
D
A
Linear Algebra - Chapter 1
Linear Combination
Can b be written as a linear combinati…
Span{}
Vector Equations
Given a set of vectors v1, v2, v3,...vp in Rn, and scalars c1…
The vector equation c1v1 + c2v2 + ... cp*vp = b can be writ…
The set of ALL linear combinations of the vectors.
c1v1 + c2v2 + ... cp*vp = b
Linear Combination
Given a set of vectors v1, v2, v3,...vp in Rn, and scalars c1…
Can b be written as a linear combinati…
The vector equation c1v1 + c2v2 + ... cp*vp = b can be writ…
Linear Algebra T1
Vector
Length of Vector
Unit Vector
scalar multiple
A real n-vector is an ordered sequence on n real #s. The set…
||a||=√a1^2+...+an^2
vector of length 1
let x=[x1...xn] be a vector in rn and let c be any scalar. th…
Vector
A real n-vector is an ordered sequence on n real #s. The set…
Length of Vector
||a||=√a1^2+...+an^2
14 terms
Linear Algebra Section 1.1
Consistent
Inconsistent
linear equation
system of linear equations
Either has one solution or infinitely many solutions
no solutions
in the variables x1...xn is an equation that can be written i…
collection of one or more linear equations involving the same…
Consistent
Either has one solution or infinitely many solutions
Inconsistent
no solutions
7 terms
Algebra 1 - Linear Functions
Slope
Y-intercept
Standard Form
Slope-intercept Form
(y₂-y₁)/(x₂-x₁)
The point where the graph crosses the y-axis. In a linear equ…
Ax + By=C, where A, B, and C are not decimals or fractions, w…
y=mx+b, where m is the slope and b is the y-intercept of the…
Slope
(y₂-y₁)/(x₂-x₁)
Y-intercept
The point where the graph crosses the y-axis. In a linear equ…
21 terms
Linear Functions (Algebra 1)
linear equation
slope
y-intercept
x-intercept
An equation in two variables whose graph in a coordinate plan…
A ratio comparing the change in output over the change in inp…
The value of the output when the input is zero (0, y). The po…
The value of the input when the output is zero (x, 0). The po…
linear equation
An equation in two variables whose graph in a coordinate plan…
slope
A ratio comparing the change in output over the change in inp…
55 terms
Introduction to Linear Algebra 1
A linear equation is...
A system of linear equations (a linear…
A solution to the linear system x_1, .…
Solving a linear system means...
variables x_1, x_2,...,x_n, any equation that can be written…
x_1,x_2,...,x_n a collection of linear equations that is the…
any ordered n-tuple (S_1,...,S_n) of real numbers if you subs…
to find the solution set, i.e. the set of all possible soluti…
A linear equation is...
variables x_1, x_2,...,x_n, any equation that can be written…
A system of linear equations (a linear…
x_1,x_2,...,x_n a collection of linear equations that is the…
26 terms
Linear Algebra Exam 1
linear equation
system of linear equations
solution
solution set
a1x1+a2x2+...+anxn=b
collection of linear equations
a list of numbers that make each equation a true statement
a set of all possible solutions
linear equation
a1x1+a2x2+...+anxn=b
system of linear equations
collection of linear equations
Linear Algebra 1.2
Reduced Echelon Form
Echelon Form
Neither
...
...
...
Reduced Echelon Form
...
Echelon Form
...
30 terms
Linear Algebra 1
vector space
subspaces
A + B
λA
Let F be a field (R or C). A vector space over F is a set V w…
Let V be a vector space. A subspace of V is a non-empty subse…
A + B := {v ∈ V | ∃a ∈ A, ∃b ∈ B : v = a + b}
λA := {v ∈ V | ∃a ∈ A : v = λa}
vector space
Let F be a field (R or C). A vector space over F is a set V w…
subspaces
Let V be a vector space. A subspace of V is a non-empty subse…
Algebra 1: Systems of Linear Equations
elimination method
linear inequality
solution of a system of linear inequal…
solution of a system of linear equations
solving systems by adding or subtracting equations to elimina…
an inequality in two variables whose graph is a region of the…
a set of values that make all inequalities in a system true.…
a set of values that make all equations in a system true. [p.…
elimination method
solving systems by adding or subtracting equations to elimina…
linear inequality
an inequality in two variables whose graph is a region of the…
10 terms
Linear Algebra 1.8
Transformation/function/mapping /T
Domain
Codomain
Range
A rule that assigns to each vector x in R^n to a vector in…
The vector space R^n on which a transformation acts.
The vector space R^m that contains (but is no necessarily exh…
The set of all possible images T(x) of transformation T.
Transformation/function/mapping /T
A rule that assigns to each vector x in R^n to a vector in…
Domain
The vector space R^n on which a transformation acts.
24 terms
Linear Algebra 1.9
Every linear transformation is...
Let T: R^n -> R^m be a linear transfor…
Standard matrix for the linear transfo…
Standard matrix for the linear transfo…
a matrix transformation (within finite dimensional spaces).
standard basis
Every linear transformation is...
a matrix transformation (within finite dimensional spaces).
Let T: R^n -> R^m be a linear transfor…
Algebra 1 - Linear Equations and Inequalities
coefficient
distributive property
equation
inequality
the numerical part of a term
for any numbers a, b, and c: a(b+c) = ab+bc
a mathematical sentence showing two expressions are equal
mathematical sentences having the symbols <,>
coefficient
the numerical part of a term
distributive property
for any numbers a, b, and c: a(b+c) = ab+bc
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