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Study sets matching "1 linear algebra math"

31 terms
Algebra 1 Linear Review
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31 terms
Algebra 1 Linear Review
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B
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A
14 terms
Algebra 1: Linear Equations
Rate of change
Slope
The Slope Formula
Positive Slope
Rate of change
Slope
31 terms
GRE MATH Linear Algebra
invertible matrix
If A and B are invertible matrices of…
formula meaning A^n is invertible
If A is an invertible matrix, then
all A such that there exists A^-1 such that AA^-1 = A^-1A = I
AB is invertible, and (AB)^-1 = B^-1A^-1
(A^n)^-1 = (A^-1)^n
A^-1 is invertible, and A^n is invertible
invertible matrix
all A such that there exists A^-1 such that AA^-1 = A^-1A = I
If A and B are invertible matrices of…
AB is invertible, and (AB)^-1 = B^-1A^-1
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…
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.…
101 terms
Math vocabulary for linear algebra
Variables... Section 1-1 variables and ex…
Algebraic expressions... Section 1-1 vari…
Factors... Section 1-1 variables and expr…
Product... Section 1-1 variables and expr…
Are symbols used to represent unspecific numbers or values. A…
Consists of one or more numbers and variables along with one…
The quantities being multiplied... Example 2x4
The outcome of what is being multiplied... Example 2x4 product i…
Variables... Section 1-1 variables and ex…
Are symbols used to represent unspecific numbers or values. A…
Algebraic expressions... Section 1-1 vari…
Consists of one or more numbers and variables along with one…
17 terms
[MATH 217: Linear Algebra] Week 1
algebra
inconsistent system
matrix
square matrix
restoration (of broken parts)
a system with no solutions
rectangular array of numbers
a matrix in which the number of columns is equal to the numbe…
algebra
restoration (of broken parts)
inconsistent system
a system with no 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…
31 terms
Algebra 1 Linear Review
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31 terms
Algebra 1 Linear Review
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70 terms
Linear Algebra Math 129 Chapters 1 and 2
In n variables; x1, x2, x3,....,xn has…
In in variables, is a set of m equatio…
1.1 DEF 1b: In this equation, a1, a2,.…
1.1 DEF 2a: A _______ of a linear equa…
linear equation
system of equations
-coefficients... -leading coefficients... -leading variable
-solution
In n variables; x1, x2, x3,....,xn has…
linear equation
In in variables, is a set of m equatio…
system of equations
21 terms
Algebra 1 Linear Equations
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31 terms
Algebra 1: Linear Review
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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
Linear Algebra Math135
Consistent System
Inconsistent System
Consistent Dependent System
Free variable
The matrix system has a solution
Matrix has no solution (last row 0 0 | non zero )
Infinite systems (last row 0 0 | 0 )
x1 x2 x3 etc can be any number, no set equation, no pivot in…
Consistent System
The matrix system has a solution
Inconsistent System
Matrix has no solution (last row 0 0 | non zero )
11 terms
Math 262 Linear Algebra
Scalar Projection
Vector Projection
‖vxw‖= ?
Scalar triple product
s = u·v/|v| = |u|cosθ
(v·d)/(‖d‖²) d
‖v‖‖w‖sinθ = Area of parallelogram determined by v and w.
u·(vxw) --> volume of parallelepiped
Scalar Projection
s = u·v/|v| = |u|cosθ
Vector Projection
(v·d)/(‖d‖²) d
100 terms
Linear Algebra (Math 3A)
Linear equation
Linear system (system of linear equati…
Solutions
Solution set
Equation that can be written in the form a₁x₁+a₂x₂+... = b
Collection of one or more linear equations involving the same…
Numbers that make each equation true
Set of all possible solutions
Linear equation
Equation that can be written in the form a₁x₁+a₂x₂+... = b
Linear system (system of linear equati…
Collection of one or more linear equations involving the same…
23 terms
Linear Algebra (Math 4C)
System of Linear Equations
Solution of a System of Linear Equations
Solution Set of a System of Linear Equ…
Equivalent Systems
A collection of m equations with the same variable quantities…
The solution of a system is a list (s1, s2, s3, ..., sn) of n…
The set of all possible solutions for a linear system.
When two linear systems have the SAME solution set.
System of Linear Equations
A collection of m equations with the same variable quantities…
Solution of a System of Linear Equations
The solution of a system is a list (s1, s2, s3, ..., sn) of n…
30 terms
Math 110 - Linear Algebra
(VS1) ... Commutativity of Addition
(VS2)... Associativity of Addition
(VS3)... Zero Vector;... Identity Element of…
(VS4)... Inverse Elements of Addition
For all x, y in V, x+y = y+x
For all x, y, z in V (x+y)+z = x+ (y+z)
There exists an element in V denoted by 0 such that x+0=x for…
For each element x in V there exists and element y in V such…
(VS1) ... Commutativity of Addition
For all x, y in V, x+y = y+x
(VS2)... Associativity of Addition
For all x, y, z in V (x+y)+z = x+ (y+z)
28 terms
Math 31 (Linear Algebra)
Thm 1
Thm 2
Linear Independence
Linear Dependence
A linear system has at least one solution if & only if the ri…
Let A be an mxn matrix coefficient matrix. Then the following…
The columns of A are linearly independent if & only if the tr…
The columns of A are linearly dependent if there is a nontriv…
Thm 1
A linear system has at least one solution if & only if the ri…
Thm 2
Let A be an mxn matrix coefficient matrix. Then the following…
48 terms
Linear Algebra MATH 313
Consistent System
Inconsistent System
Row Equivalent Matrices
Linear Combination
The system has either 1 solution or infinitely many
The system has no solutions
If a sequence of Elementary Row Operations can transform one…
Given vectors in R^n and scalars c1....cp, the vector b is gi…
Consistent System
The system has either 1 solution or infinitely many
Inconsistent System
The system has no solutions
43 terms
Linear Algebra MATH 13
Elementary row operations
Equivalent systems of linear equations
Matrix in row-echelon form properties
Matrix in reduced row-echelon form pro…
1. Interchange two rows... 2. Multiply a row by a nonzero consta…
Systems that have the same solution set
1. Rows of only zeros are at the bottom... 2. For each row that'…
It's in row-echelon form and every column that has a leading…
Elementary row operations
1. Interchange two rows... 2. Multiply a row by a nonzero consta…
Equivalent systems of linear equations
Systems that have the same solution set
16 terms
Math 340 Linear Algebra
Linear system
What are two basic methods of solving…
Two systems of linear equations are eq…
How do we know the method of eliminati…
A set of linear equations.
Method of elimination and substitution.
If they have the same solutions.
Each step in the method of elimination gives an equivalent sy…
Linear system
A set of linear equations.
What are two basic methods of solving…
Method of elimination and substitution.
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...
41 terms
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
32 terms
Math 1553 - linear algebra KNOW
x bar parallel is
two vectors are orthogonal to each oth…
magnitude is
In an LU decomposition, the columns of…
the orthogonal projection of x bar onto the line
u * v = 0
the square root of each component squared
the pivotal columns in original matrix
x bar parallel is
the orthogonal projection of x bar onto the line
two vectors are orthogonal to each oth…
u * v = 0
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
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.
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
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
14 terms
Algebra 1: Linear (w/ pictures)
Rate of change
Slope
The Slope Formula
Positive Slope
Rate of change
Slope
15 terms
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
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
64 terms
Algebra 1: Linear and Inequality Review
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7 terms
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…
11 terms
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…
13 terms
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…
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…
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 1.3
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.
15 terms
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
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.
32 terms
Linear Algebra1
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.…
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…
17 terms
Linear Systems of Equations (Algebra 1)
Function
Function Notation
Input
Output
A relationship where each input has exactly one output.
If x is input and y is the output, then the function notation…
A number in the domain of a function. ... The independent variab…
A number in the range of a function.... The dependent variable.
Function
A relationship where each input has exactly one output.
Function Notation
If x is input and y is the output, then the function notation…
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
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
44 terms
Linear Algebra Chapter 1
Vector
Problem with definitions (6th Grade Ex…
Infusing Tech into Math Article
Velocity
a. Math. A quantity having direction as well as magnitude, de…
The truth is that all definitions, by their very nature, tend…
1) the student teachers' attitudes about using technology in…
Knowing that a ship has a speed of 10 knots (nautical miles p…
Vector
a. Math. A quantity having direction as well as magnitude, de…
Problem with definitions (6th Grade Ex…
The truth is that all definitions, by their very nature, tend…
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
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