Study sets matching "algebra linear equations chapter 7"
Study sets
Diagrams
Classes
Users
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
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
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…
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.
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…
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
Formula
Solve an Equation
Equivalent Equations
Multi-Step Equations
A mathematical relationship or rule expressed in symbols.
The process of finding all values of the variable that make th…
equations that have the same solution
Equations with more than one operation.
Formula
A mathematical relationship or rule expressed in symbols.
Solve an Equation
The process of finding all values of the variable that make th…
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
x<-9
8
(1, 1)
x<2 or x >20
Solve this inequality:... (hint: flip the symbol when you ÷ or ×…
Solve for x:... 4(x-5)=12
What is the solution?... y=4x-3... y=-5x+6
Solve this compound "or" inequality:... 5x<10 or .5x>10
x<-9
Solve this inequality:... (hint: flip the symbol when you ÷ or ×…
8
Solve for x:... 4(x-5)=12
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…
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
Constant Term
Coefficient
Variable
Slope-intercept form
In Algebra, a constant is a number on its own, or sometimes a…
A number used to multiply a variable.
A symbol for a number we don't know yet. It is usually a lette…
A way to express the equation of a line. In general, the formu…
Constant Term
In Algebra, a constant is a number on its own, or sometimes a…
Coefficient
A number used to multiply a variable.
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.
x<-9
8
(1, 1)
x<2 or x >20
Solve this inequality:... (hint: flip the symbol when you ÷ or ×…
Solve for x:... 4(x-5)=12
What is the solution?... (hint: 2nd, CALC, 5, enter, enter, enter…
Solve this compound "or" inequality:... 5x<10 or .5x>10
x<-9
Solve this inequality:... (hint: flip the symbol when you ÷ or ×…
8
Solve for x:... 4(x-5)=12