# Study sets matching "algebra linear equations chapter 7"

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

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 ce…

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

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…

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…

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…

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.

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…