# Study sets matching "algebra linear equations chapter 7"

Study sets

Diagrams

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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