#### 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…

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

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

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

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.

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

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…

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Multiplication Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

If a = b, then a + c = b + c. Adding equal amounts to each si…

If a = b and c does not equal 0, then a/c = b/c. Dividing eac…

If A = B, then A

**C = B**C. Multiplying each side of an equatio…Subtraction Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

Addition Property of Equality

If a = b, then a + c = b + c. Adding equal amounts to each si…

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…

Linear Equation

Linear System

Solution

Solution Set

An equation that can be written in the form:... a1x1+a2x2+...+an…

A collection of one or more linear equations involving the sa…

A list (s1, s2, ..., sn) of numbers that makes each equation…

The set of all possible solutions for a given system

Linear Equation

An equation that can be written in the form:... a1x1+a2x2+...+an…

Linear System

A collection of one or more linear equations involving the sa…

linear equation

slope

y-intercept

x-intercept

An equation in two variables whose graph is a straight line.

The steepness of a line. A ratio comparing the change in y ov…

The point where a graph crosses the y-axis. The value of the…

The point where a graph crosses the x-axis. The value of the…

linear equation

An equation in two variables whose graph is a straight line.

slope

The steepness of a line. A ratio comparing the change in y ov…

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 t…

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 t…

slope intercept form

point slope form

y - intercept

How to Write a Linear Function... Ex: Wri…

where m is the slope and (x1, y1) is a point on the line... Thi…

the y-coordinate of the point where the line crosses the y-axis

1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17)... 2 - Cal…

slope intercept form

point slope form

where m is the slope and (x1, y1) is a point on the line... Thi…

Formula

Multi step equations

Identity

Ratio

Any equation that states a rule for the relationship between…

An Equation with more than one step

An equation with a variable has infinite possibilities

A comparison of two numbers by division

Formula

Any equation that states a rule for the relationship between…

Multi step equations

An Equation with more than one step

When is a system of linear equations c…

When is a system of linear equations i…

When do 2 linear systems have the same…

(Row) Echelon Form

When it has either one solution or infinitely many solutions

When it has no solution

If their augmented matrices are row equivalent

1) All nonzero rows are above any rows of all zeros... 2) Each l…

When is a system of linear equations c…

When it has either one solution or infinitely many solutions

When is a system of linear equations i…

When it has no solution

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

conjecture

theorem or rule

equation

linear equation in one variable

an unproven statement about a general mathematical concept

a proven statement about a general mathematical concept

a statement that two expressions are equal

an equation that can be written in the form ax + b = 0, where…

conjecture

an unproven statement about a general mathematical concept

theorem or rule

a proven statement about a general mathematical concept

linear equation

expression

equation

coefficient

An equation in two variables whose graph in a coordinate plan…

A mathematical sentence without an equal sign.

A mathematical sentence that contains an equal sign.

A number multiplied by a variable in an algebraic expression…

linear equation

An equation in two variables whose graph in a coordinate plan…

expression

A mathematical sentence without an equal sign.

Graphically, a system of equations has…

Graphically, a system of equations has…

The three possible solutions for a sys…

A system has infinite solutions if:

They are parallel lines. They never intersect so there's no w…

at the point of intersection. The point where lines have a co…

- 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 w…

Graphically, a system of equations has…

at the point of intersection. The point where lines have a co…

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…

slope-intercept form

best-fitting line

correlation

point-slope form

y=mx+b

the equation of a line that best follows a set of data

A measure of the relationship between two variables

y-y1=m(x-x1)

slope-intercept form

y=mx+b

best-fitting line

the equation of a line that best follows a set of data

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

parallel lines

perpendicular lines

linear inequality in two variables

solution of an inequality in two varia…

Two different non-vertical lines that have the same slope

Two non-vertical lines in the same plane whose slopes have a…

Can be written in one of the following forms: Ax + By < C, Ax…

One or more ordered pairs that make the inequality true.

parallel lines

Two different non-vertical lines that have the same slope

perpendicular lines

Two non-vertical lines in the same plane whose slopes have a…

solve an equation

equivalent equations

linear equation

linear equation with two variables

find values that satisfy the equation

two equations that have the same solutions

one or more variables in which each term in the equation is e…

solved by an ordered pair; (x,y)

solve an equation

find values that satisfy the equation

equivalent equations

two equations that have the same solutions

Subtraction Property of Equality

Addition Property of Equality

Division Property of Equality

Multiplication Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

If a = b, then a + c = b + c. Adding equal amounts to each si…

If a = b and c does not equal 0, then a/c = b/c. Dividing eac…

If A = B, then A

**C = B**C. Multiplying each side of an equatio…Subtraction Property of Equality

If a = b, then a - c = b - c. Subtracting equal amounts from…

Addition Property of Equality

If a = b, then a + c = b + c. Adding equal amounts to each si…

formula

two-step equation

perimeter

area

an equation that shows the relationship among certain quantit…

two different operations

distance around a geometric figure

the measure of the surface enclosed by a rectangle

formula

an equation that shows the relationship among certain quantit…

two-step equation

two different operations