# Study sets matching "algebra linear equations chapter 7"

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Determine if given matrix is symetric

determine if is the matrix is orthogona…

Orthogonally diagonalize the matrix, gi…

Find the matrix of the quadratic form.…

transposed matrix is EXACTLY the same

test for orthogonal UtranspU=Identity matrix

A=PDPtrans if orth and symetric... 1. use eigenvalues to find ei…

rewrite into matrix directly... a. [12 29/2]... ......[29/2 15... b. […

Determine if given matrix is symetric

transposed matrix is EXACTLY the same

determine if is the matrix is orthogona…

test for orthogonal UtranspU=Identity matrix

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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

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

absolute-value equation

algebraic equation

closed sentence

open sentence

a number sentence that contains an equal sign and algebraic ex…

contains no variable and is either true or false

contains variables and an equal sign, and is neither true nor…

absolute-value equation

algebraic equation

a number sentence that contains an equal sign and algebraic ex…

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

Algebraic expression

Coefficient

Common denominator

Constant

an expression that contains at least one variable

the number that is multiplied by the variable in an algebraic…

a denominator that is the same in two or more fractions

a value that does not change

Algebraic expression

an expression that contains at least one variable

Coefficient

the number that is multiplied by the variable in an algebraic…

absolute value equation

correlation coefficient

line of best fit

linear equation

Equation whose graph forms a V that opens up or down.

A number that tells how closely the equation of best fit model…

The most accurate trend line on a scatter plot showing the rel…

An equation whose graph forms a straight line.

absolute value equation

Equation whose graph forms a V that opens up or down.

correlation coefficient

A number that tells how closely the equation of best fit model…

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

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…

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

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.

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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…