Study sets matching "algebra linear equations chapter 7"
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Classes
Users
Scatterplot
Line of Best Fit
Positive Association
Negative Association
A graph in which the values of two variables are plotted along…
A straight line drawn through the center of a group of data po…
One variable increases as the other variable increases
One variable increases as the other variable decreases
Scatterplot
A graph in which the values of two variables are plotted along…
Line of Best Fit
A straight line drawn through the center of a group of data po…
slope
y-intercept
x-intercept
scatter plot
ration of the vertical change (rise) to the horizontal change…
where a point crosses the y axis
where point crosses the x-axis
graph that shows the general relationship between 2 sets of da…
slope
ration of the vertical change (rise) to the horizontal change…
y-intercept
where a point crosses the y axis
Eigenspace of λ
Definition of a Diagonalizable Matrix
Condition for Diagonalization
Definition of Symmetric Matrix
If A is an nxn matrix with an eigenvalue λ, then the set of al…
An nxn matrix A is Diagonalizable when A is similar to a diago…
If an nxn matrix A has n linearly independent eigenvectors, th…
A square matrix A is symmetric when it is equal to its transpo…
Eigenspace of λ
If A is an nxn matrix with an eigenvalue λ, then the set of al…
Definition of a Diagonalizable Matrix
An nxn matrix A is Diagonalizable when A is similar to a diago…
Consecutive integers
Equivalent equations
Formula
Identity
Integers in counting order
Equations that have the same solution.
An equation that states a rule for the relationship between ce…
An equation that is true for every value of the variable.
Consecutive integers
Integers in counting order
Equivalent equations
Equations that have the same solution.
coordinate plane
origin
x-axis
y-axis
the grid created by the horizontal x-axis and the vertical y-a…
(0,0) in the coordinate plane; center of the grid
the horizontal number line in the coordinate plane (left to ri…
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-a…
origin
(0,0) in the coordinate plane; center of the grid
Graphically, a system of equations has…
Graphically, a system of equations has…
The three possible solutions for a syst…
A system has infinite solutions if:
They are parallel lines. They never intersect so there's no wa…
at the point of intersection. The point where lines have a com…
- no solution... - infinite solutions ... - a unique solution
The equations are equal.... Same slope and y-intercept.
Graphically, a system of equations has…
They are parallel lines. They never intersect so there's no wa…
Graphically, a system of equations has…
at the point of intersection. The point where lines have a com…
Inverse Operations
Two-Step Equation
Solution
Coefficient
Operations that "undo" each other. Ex. Adding 3 and subtractin…
An equation that requires two inverse operations to solve.
Any value for a variable that makes the equation true.
The number that is multiplied by the variable.
Inverse Operations
Operations that "undo" each other. Ex. Adding 3 and subtractin…
Two-Step Equation
An equation that requires two inverse operations to solve.
Multiplying by the Reciprocal
Inverse Operations
Two-Step Equation
Solution
When you multiply a term with a fractional coefficient by the…
Operations that "undo" each other. For example, adding 3 and s…
Equations that require two inverse operations to solve.
Any value for a variable that makes the equation true.
Multiplying by the Reciprocal
When you multiply a term with a fractional coefficient by the…
Inverse Operations
Operations that "undo" each other. For example, adding 3 and s…
affine transformation
augmented matrix
back substitution
basic variable
similar to a linear transformation, but does not necessarily p…
a matrix made up of a coefficient matrix for a linear system a…
phase of row reduction which transforms an echelon matrix to a…
a variable in the linear system that corresponds to a pivot co…
affine transformation
similar to a linear transformation, but does not necessarily p…
augmented matrix
a matrix made up of a coefficient matrix for a linear system a…
Vector Space
Additive Inverse
Span
P
a vector space consists of a set V of vectors together with op…
opposite so that A+(-A)=0
set of all linear combinations of the form c1v1+c2v2+...+cmvm
the set of polynomials with real coefficents
Vector Space
a vector space consists of a set V of vectors together with op…
Additive Inverse
opposite so that A+(-A)=0
What is a linear equation?
What is a system of linear equations?
What is a solution of a linear equation?
What is a solution set?
Any equation that can be written in the following form: (pg. 2)
A system of linear equations (or a linear system) is a collect…
A list of numbers that satisfies a system of linear equations.…
The set of all possible solutions is called the solution set o…
What is a linear equation?
Any equation that can be written in the following form: (pg. 2)
What is a system of linear equations?
A system of linear equations (or a linear system) is a collect…
An nxn matrix that is orthogonally diag…
If A^T = A and if vectors u and v satis…
An n x n symmetric matrix has n distinc…
For a nonzero v in R^n, the matrix vv^T…
True
True
False, there are n eigenvalues, but the eigenvalues do not hav…
False
An nxn matrix that is orthogonally diag…
True
If A^T = A and if vectors u and v satis…
True
a. The matrix of a quadratic form is a…
b. A quadratic form has no cross-produc…
c. The principal axes of a quadratic fo…
d. A positive definite quadratic form Q…
True
True
True
False, Q(x) = 0 when x = 0
a. The matrix of a quadratic form is a…
True
b. A quadratic form has no cross-produc…
True
slope
slope triangle
rise
run
the ratio of rise over run of a line; its steepness or flatness
a triangle drawn to show rise and run
the amount of change on the y-coordinates
the amount of change on the x-coordinates
slope
the ratio of rise over run of a line; its steepness or flatness
slope triangle
a triangle drawn to show rise and run
coordinate plan
ordered pair
quadrants
x-axis
A plane formed by two numbers lines that intersect at right an…
Two numbers that identify the location of a point.
The four parts into which the coordinate plane is divided by i…
The horizontal axis of the coordinate plane.
coordinate plan
A plane formed by two numbers lines that intersect at right an…
ordered pair
Two numbers that identify the location of a point.
consistent
dependent
elimination
inconsistent
a system of linear equations that has at least one ordered pai…
a system of linear equations that has an infinite number of so…
the use of addition or subtraction to eliminate one variable a…
a system of equations with no ordered pair that satisfies both…
consistent
a system of linear equations that has at least one ordered pai…
dependent
a system of linear equations that has an infinite number of so…
Linear Equation
Linear System
Solution
Solution Set
An equation that can be written in the form:... a1x1+a2x2+...+anx…
A collection of one or more linear equations involving the sam…
A list (s1, s2, ..., sn) of numbers that makes each equation a…
The set of all possible solutions for a given system
Linear Equation
An equation that can be written in the form:... a1x1+a2x2+...+anx…
Linear System
A collection of one or more linear equations involving the sam…
Expression
equation
ways that you can simplify expressions
equation exprlanation
do not contain an equals sign.
contain and equal sign.
1. combine like terms ... 2. find a common denominator ... 3. pull o…
Equation is like a weight of justice. whatever you do on one s…
Expression
do not contain an equals sign.
equation
contain and equal sign.