# Study sets matching "linear algebra chapter 1"

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Classes

Users

Absolute Value

Integer

Exponent

Function

a number's distance from zero

positive and negative whole numbers

tells how many times to multiply the base number

a relationship where the input determines the output

Absolute Value

a number's distance from zero

Integer

positive and negative whole numbers

C.The solution set is empty.

C. The solution set contains one solut…

A. The matrix is the augmented matrix o…

Is the statement "Two matrices are row…

A. The solution set has exactly one element, left parenthesis…

A. The solution has infinitely many elements.... B. The solution…

Determine the value(s) of h such that the matrix is the augme…

C. False, because if two matrices are row equivalent it means…

C.The solution set is empty.

A. The solution set has exactly one element, left parenthesis…

C. The solution set contains one solut…

A. The solution has infinitely many elements.... B. The solution…

A linear equation in the variables x_1.…

coeffecients

System of linear equations

Solution

a_1x_1 + a_2x_2 +...+a_nx_n = b

real or complex numbers usually known in advance (a_1...a_n)

also known as a linear system is a collection of one or more l…

A solution of the system is a list of numbers (s_1...s_n) that…

A linear equation in the variables x_1.…

a_1x_1 + a_2x_2 +...+a_nx_n = b

coeffecients

real or complex numbers usually known in advance (a_1...a_n)

Linear Equation

System of Linear Equations

Solution of System

Linear Systems

a1x1+a2x2+...+anxn=b ... b and coefficients are real numbers

collection of one or more linear equations with the same varia…

Ordered list of numbers which make each of the equations true…

can be: ... -no sol'n (inconsistent)... -1 sol'n (consistent, unique…

Linear Equation

a1x1+a2x2+...+anxn=b ... b and coefficients are real numbers

System of Linear Equations

collection of one or more linear equations with the same varia…

Linear Equation

System of Linear Equations

Solution

Solution Set

describes a firsrt order line in Rn equations of the form a1x1…

collection of 1+ linear equations to be solved simultaneously

a set of real numbers s1...sn such that each equation holds if…

a set of all solutions in a system

Linear Equation

describes a firsrt order line in Rn equations of the form a1x1…

System of Linear Equations

collection of 1+ linear equations to be solved simultaneously

The number of solutions in a system of…

A system is said to be CONSISTENT if...

A system is said to be INCONSISTENT if.…

Echelon Form

None, One, or Infinitely Many

it has one or infinitely many solutions

it has no solution

1- rows of zeroes on the bottom, 2- each leading entry of a ro…

The number of solutions in a system of…

None, One, or Infinitely Many

A system is said to be CONSISTENT if...

it has one or infinitely many solutions

solutions of a linear system

(1.1) linear system

elementary row operations

echelon form

none, one, or infinitely many

a linear system is consistent if it has a solution

replacement - replace one row by the sum of itself and another…

1. all nonzero rows are above any rows of all zeros... 2. each le…

solutions of a linear system

none, one, or infinitely many

(1.1) linear system

a linear system is consistent if it has a solution

If two systems of linear equations have…

Solution set

Linear systems can have ___________ sol…

Elementary Row Operations

they are equivalent

all possible solutions to linear equation

no, exactly one, infinitely many

add a multiple of one row to an existing row, interchange rows…

If two systems of linear equations have…

they are equivalent

Solution set

all possible solutions to linear equation

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

Problem with definitions (6th Grade Exa…

Infusing Tech into Math Article

Velocity

a. Math. A quantity having direction as well as magnitude, den…

The truth is that all definitions, by their very nature, tend…

1) the student teachers' attitudes about using technology in c…

Knowing that a ship has a speed of 10 knots (nautical miles pe…

Vector

a. Math. A quantity having direction as well as magnitude, den…

Problem with definitions (6th Grade Exa…

The truth is that all definitions, by their very nature, tend…

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…

Linear Equation

Coefficient Matrix

Augmented Matrix

Row operations (3)

a₁x₁+...+anxn=b

|a₁₁ a₁₂ a₁₃|... |a₂₁ a₂₂ a₂₃|... |a₃₁ a₃₂ a₃₃|

|a₁₁ a₁₂ a₁₃ b₁|... |a₂₁ a₂₂ a₂₃ b₂|... |a₃₁ a₃₂ a₃₃ b₃|

switch rows, multiply row by scalar, add multiple of row to ot…

Linear Equation

a₁x₁+...+anxn=b

Coefficient Matrix

|a₁₁ a₁₂ a₁₃|... |a₂₁ a₂₂ a₂₃|... |a₃₁ a₃₂ a₃₃|

linear system

the span of a set of vectors

a set of vectors spans Rn

a system of linear equations is homogen…

is consistent if it has a solution

is the set of all linear combinations of the vectors. The Span…

if every vector inRncan be written as a linear combination of…

a form Ax=0 for some matrix A

linear system

is consistent if it has a solution

the span of a set of vectors

is the set of all linear combinations of the vectors. The Span…

solutions of a linear system

(1.1) linear system

elementary row operations

echelon form

none, one, or infinitely many

a linear system is consistent if it has a solution

replacement - replace one row by the sum of itself and another…

1. all nonzero rows are above any rows of all zeros... 2. each le…

solutions of a linear system

none, one, or infinitely many

(1.1) linear system

a linear system is consistent if it has a solution

Theorem: Each matrix is row equivalent…

Theorem: A linear system is consistent…

Theorem: If a linear system is consiste…

Span:

one and only one reduced echelon matrix.

the rightmost column of the augmented matrix is NOT a pivot co…

every column in the coefficient matrix is a pivot column.

the set of all linear combinations of given vectors

Theorem: Each matrix is row equivalent…

one and only one reduced echelon matrix.

Theorem: A linear system is consistent…

the rightmost column of the augmented matrix is NOT a pivot co…

Linear Equation

System of Linear Equations

Solution

Solution Set

describes a firsrt order line in Rn equations of the form a1x1…

collection of 1+ linear equations to be solved simultaneously

a set of real numbers s1...sn such that each equation holds if…

a set of all solutions in a system

Linear Equation

describes a firsrt order line in Rn equations of the form a1x1…

System of Linear Equations

collection of 1+ linear equations to be solved simultaneously

Pivot position

Theorem 2

Linear combination

Span

a location in A that corresponds to a leading 1 in the reduced…

A linear system is consistent if and only if the rightmost col…

Any sum of c1v1+c2v2+...ckvk where c1,c2...are in Rm

All possible linear combinations of v1,...,vk

Pivot position

a location in A that corresponds to a leading 1 in the reduced…

Theorem 2

A linear system is consistent if and only if the rightmost col…

equivalent

solution set

consistent

inconsistent

Two linear systems are called equivalent if they have the same…

the set of all possible solutions of a linear system

A system of linear equations is said to be consistent if it ha…

A system of linear equations is inconsistent if it has no solu…

equivalent

Two linear systems are called equivalent if they have the same…

solution set

the set of all possible solutions of a linear system

Linear Equation

Linear System

Coefficient Matrix

Augmented Matrix

An equation which can be written as a1x1+...+anXn=b where b an…

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

A matrix with the coefficients from the linear equations/Linea…

The Coefficient matrix with an added column containing the con…

Linear Equation

An equation which can be written as a1x1+...+anXn=b where b an…

Linear System

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

If the rank(A) <= m and the rank(A) <= n

If the rank(A) = m

If the rank(A) = n

If rank(A) < n

The number of free variables = n - rank(A)

System is consistent

System has at most 1 solution

0 solutions or infinite solutions

If the rank(A) <= m and the rank(A) <= n

The number of free variables = n - rank(A)

If the rank(A) = m

System is consistent