# 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

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

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

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…

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-intercept form

slope-point form

general form

standard form

y=mx+b, where m is the slope and b is the y-intercept of the l…

The equation of a line in the form y - y1 = m (x - x1).... m is t…

Ax+By+C=0; A is a whole number.

Ax+By=C; A is a whole number.

slope-intercept form

y=mx+b, where m is the slope and b is the y-intercept of the l…

slope-point form

The equation of a line in the form y - y1 = m (x - x1).... m is t…

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…

unitarily similar matrices A and B (wit…

Schur form

unitary matrix

normal matrix

A=UBU*

upper triangular matrix T=U*AU;... square matrix A is unitarily s…

1) orthonormal columns... 2) orthonormal rows... 3) U*=U^-1 (conjuga…

A

**A=AA**unitarily similar matrices A and B (wit…

A=UBU*

Schur form

upper triangular matrix T=U*AU;... square matrix A is unitarily s…

(-3, 7)

(1, -6)

8√2

√173

Find the midpoint of the segment with endpoints (-8, 3) and (2…

Find the midpoint of the segment with endpoints (-3, -3) and (…

Determine the distance between (5, 6) and (-3, -2)

Determine the distance between (4, 6) and (2, -7)

(-3, 7)

Find the midpoint of the segment with endpoints (-8, 3) and (2…

(1, -6)

Find the midpoint of the segment with endpoints (-3, -3) and (…

Constant Term

Coefficient

Variable

Slope-intercept form

In Algebra, a constant is a number on its own, or sometimes a…

A number used to multiply a variable.

A symbol for a number we don't know yet. It is usually a lette…

A way to express the equation of a line. In general, the formu…

Constant Term

In Algebra, a constant is a number on its own, or sometimes a…

Coefficient

A number used to multiply a variable.