#### 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 da…

slope

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

y-intercept

where a point crosses the y axis

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

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…

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…

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 n…

= 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 n…

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.

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…

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…

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…

quadrant

abscissa

ordinate

ordered pair

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

The x-coordinate of an ordered pair.

The y-coordinate of an ordered pair.

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

quadrant

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

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 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

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

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…

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.

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.

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 con…

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

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

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 con…