#### Study sets matching "algebra linear equations chapter 7"

#### Study sets matching "algebra linear equations chapter 7"

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 d…

slope

ration of the vertical change (rise) to the horizontal change…

y-intercept

where a point crosses the y axis

Literal Equations

Complex Numbers

The Complex Number √-1

The Complex Number i^2

equations that are all or mostly all variables

a number written in the form (a + bi) where a and b are Real…

= i

= -1

Literal Equations

equations that are all or mostly all variables

Complex Numbers

a number written in the form (a + bi) where a and b are Real…

Consecutive integers

Equivalent equations

Extremes

Formula

Integers in counting order

Equations that have the same solution.

In the ratio a/b = c/d, the a and d.

An equation that states a rule for the relationship between c…

Consecutive integers

Integers in counting order

Equivalent equations

Equations that have the same solution.

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…

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…

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

Inverse Operations

Two-Step Equation

Solution

Coefficient

Operations that "undo" each other. Ex. Adding 3 and subtracti…

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 subtracti…

Two-Step Equation

An equation that requires two inverse operations to solve.

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 a…

An nxn matrix A is Diagonalizable when A is similar to a diag…

If an nxn matrix A has n linearly independent eigenvectors, t…

A square matrix A is symmetric when it is equal to its transp…

Eigenspace of λ

If A is an nxn matrix with an eigenvalue λ, then the set of a…

Definition of a Diagonalizable Matrix

An nxn matrix A is Diagonalizable when A is similar to a diag…

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 collec…

A list of numbers that satisfies a system of linear equations…

The set of all possible solutions is called the solution set…

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 collec…

quadrant

abscissa

ordinate

ordered pair

One of 4 regions of the coordinate plane formed by the inters…

The x-coordinate of an ordered pair.

The y-coordinate of an ordered pair.

Describes a location on the coordinate plane, with the x-coor…

quadrant

One of 4 regions of the coordinate plane formed by the inters…

abscissa

The x-coordinate of an ordered pair.

Vector Space

Additive Inverse

Span

P

a vector space consists of a set V of vectors together with o…

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 o…

Additive Inverse

opposite so that A+(-A)=0

a. The matrix of a quadratic form is a…

b. A quadratic form has no cross-produ…

c. The principal axes of a quadratic f…

d. A positive definite quadratic form…

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-produ…

True

An nxn matrix that is orthogonally dia…

If A^T = A and if vectors u and v sati…

An n x n symmetric matrix has n distin…

For a nonzero v in R^n, the matrix vv^…

True

True

False, there are n eigenvalues, but the eigenvalues do not ha…

False

An nxn matrix that is orthogonally dia…

True

If A^T = A and if vectors u and v sati…

True

consistent

dependent

elimination

inconsistent

a system of linear equations that has at least one ordered pa…

a system of linear equations that has an infinite number of s…

the use of addition or subtraction to eliminate one variable…

a system of equations with no ordered pair that satisfies bot…

consistent

a system of linear equations that has at least one ordered pa…

dependent

a system of linear equations that has an infinite number of s…

coordinate plan

ordered pair

quadrants

x-axis

A plane formed by two numbers lines that intersect at right a…

Two numbers that identify the location of a point.

The four parts into which the coordinate plane is divided by…

The horizontal axis of the coordinate plane.

coordinate plan

A plane formed by two numbers lines that intersect at right a…

ordered pair

Two numbers that identify the location of a point.

Inverse Operations

Equivalent Equations

Identity

Ratio

Two operations that undo each other.

Equations that have the same solutions.

An equation that is true for all values of the variable.

A comparison of two numbers using division.

Inverse Operations

Two operations that undo each other.

Equivalent Equations

Equations that have the same solutions.

The Rectangular Coordinate System

On the x-axis

On the y-axis

We can represent a specific location,…

is made up of a horizontal number line and a vertical number…

the positive direction is to the right and the negative direc…

the positive direction is up and the negative direction is do…

These two numbers make up an ordered pair; we write an ordere…

The Rectangular Coordinate System

is made up of a horizontal number line and a vertical number…

On the x-axis

the positive direction is to the right and the negative direc…

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

Point-Slope Form

Converse of a conditional

Perpendicular Lines

Scatter Plot

An equation of a non-vertical line written in form y-y1 = m(x…

A statement formed by interchanging the hypothesis and the co…

Two lines in the same plane that intersect to form a right an…

A graph used to determine whether there is a relationship or…

Point-Slope Form

An equation of a non-vertical line written in form y-y1 = m(x…

Converse of a conditional

A statement formed by interchanging the hypothesis and the co…