#### Study sets matching "1 linear algebra math"

#### Study sets matching "1 linear algebra math"

linear equation

slope

y-intercept

x-intercept

An equation in two variables whose graph in a coordinate plan…

A ratio comparing the change in output over the change in inp…

The value of the output when the input is zero (0, y). The po…

The value of the input when the output is zero (x, 0). The po…

linear equation

An equation in two variables whose graph in a coordinate plan…

slope

A ratio comparing the change in output over the change in inp…

invertible matrix

If A and B are invertible matrices of…

formula meaning A^n is invertible

If A is an invertible matrix, then

all A such that there exists A^-1 such that AA^-1 = A^-1A = I

AB is invertible, and (AB)^-1 = B^-1A^-1

(A^n)^-1 = (A^-1)^n

A^-1 is invertible, and A^n is invertible

invertible matrix

all A such that there exists A^-1 such that AA^-1 = A^-1A = I

If A and B are invertible matrices of…

AB is invertible, and (AB)^-1 = B^-1A^-1

linear equation

slope

Types of Slope

y-intercept

An equation in two variables whose graph in a coordinate plan…

A ratio comparing the change in output over the change in inp…

The value of the output when the input is zero (0, y). The po…

linear equation

An equation in two variables whose graph in a coordinate plan…

slope

A ratio comparing the change in output over the change in inp…

Variables... Section 1-1 variables and ex…

Algebraic expressions... Section 1-1 vari…

Factors... Section 1-1 variables and expr…

Product... Section 1-1 variables and expr…

Are symbols used to represent unspecific numbers or values. A…

Consists of one or more numbers and variables along with one…

The quantities being multiplied... Example 2x4

The outcome of what is being multiplied... Example 2x4 product i…

Variables... Section 1-1 variables and ex…

Are symbols used to represent unspecific numbers or values. A…

Algebraic expressions... Section 1-1 vari…

Consists of one or more numbers and variables along with one…

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 r…

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

Vector Space

Vector Space Axioms

Subspace

Transpose

a set where addition and scalar multiplication as well as the…

1. Commutativity of addition... 2. Associativity in addition... 3.…

a subset of a vector space that is also a vector space closed…

Matrix formed from switching rows and colums (A₁₂)'=A₂₁

Vector Space

a set where addition and scalar multiplication as well as the…

Vector Space Axioms

1. Commutativity of addition... 2. Associativity in addition... 3.…

x-axis

y-axis

domain

range

the horizontal axis of the coordinate plane.

the vertical axis of the coordinate plane.

the input of the function (x-values).

the output of the function (y-values).

x-axis

the horizontal axis of the coordinate plane.

y-axis

the vertical axis of the coordinate plane.

coordinate plane

origin

x-axis

y-axis

the grid created by the horizontal x-axis and the vertical y-…

(0,0) in the coordinate plane; center of the grid

the horizontal number line in the coordinate plane (left to r…

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-…

origin

(0,0) in the coordinate plane; center of the grid

Quadrant

Solution of an equation in two variables

Graph of an equation in two variables

Linear equation

One of the four regions into which the x and y axes divide th…

An ordered pair that produces a true statement when the coord…

The set of points in a coordinate plane that represent all so…

An equation whose graph is a line.

Quadrant

One of the four regions into which the x and y axes divide th…

Solution of an equation in two variables

An ordered pair that produces a true statement when the coord…

In n variables; x1, x2, x3,....,xn has…

In in variables, is a set of m equatio…

1.1 DEF 1b: In this equation, a1, a2,.…

1.1 DEF 2a: A _______ of a linear equa…

linear equation

system of equations

-coefficients... -leading coefficients... -leading variable

-solution

In n variables; x1, x2, x3,....,xn has…

linear equation

In in variables, is a set of m equatio…

system of equations

linear equation

system of linear equations (linear sys…

solution

A system of linear equations has

an equation that can be written in the form ax+ax+ax+...+ax=b…

a collection of one or more linear equations involving the sa…

A solution of the system is a list (s,s,s,s..,s) of numbers t…

1. no solution... 2. exactly one solution... 3. infinitely many sol…

linear equation

an equation that can be written in the form ax+ax+ax+...+ax=b…

system of linear equations (linear sys…

a collection of one or more linear equations involving the sa…

equivalent system of equations

A Homogeneous system

invertible matrix

singularity

when two system of equations have the same solution set

when the constants on the right hand side of the matrix are a…

when there exists a matrix B such that AB=BA=I.

when a nxn matrix does not have a multiplicative inverse.

equivalent system of equations

when two system of equations have the same solution set

A Homogeneous system

when the constants on the right hand side of the matrix are a…

System of Linear Equations

Solution of a System of Linear Equations

Solution Set of a System of Linear Equ…

Equivalent Systems

A collection of m equations with the same variable quantities…

The solution of a system is a list (s1, s2, s3, ..., sn) of n…

The set of all possible solutions for a linear system.

When two linear systems have the SAME solution set.

System of Linear Equations

A collection of m equations with the same variable quantities…

Solution of a System of Linear Equations

The solution of a system is a list (s1, s2, s3, ..., sn) of n…

(VS1) ... Commutativity of Addition

(VS2)... Associativity of Addition

(VS3)... Zero Vector;... Identity Element of…

(VS4)... Inverse Elements of Addition

For all x, y in V, x+y = y+x

For all x, y, z in V (x+y)+z = x+ (y+z)

There exists an element in V denoted by 0 such that x+0=x for…

For each element x in V there exists and element y in V such…

(VS1) ... Commutativity of Addition

For all x, y in V, x+y = y+x

(VS2)... Associativity of Addition

For all x, y, z in V (x+y)+z = x+ (y+z)

algebra

inconsistent system

matrix

square matrix

restoration (of broken parts)

a system with no solutions

rectangular array of numbers

a matrix in which the number of columns is equal to the numbe…

algebra

restoration (of broken parts)

inconsistent system

a system with no solutions

Consistent System

Inconsistent System

Row Equivalent Matrices

Linear Combination

The system has either 1 solution or infinitely many

The system has no solutions

If a sequence of Elementary Row Operations can transform one…

Given vectors in R^n and scalars c1....cp, the vector b is gi…

Consistent System

The system has either 1 solution or infinitely many

Inconsistent System

The system has no solutions

Thm 1

Thm 2

Linear Independence

Linear Dependence

A linear system has at least one solution if & only if the ri…

Let A be an mxn matrix coefficient matrix. Then the following…

The columns of A are linearly independent if & only if the tr…

The columns of A are linearly dependent if there is a nontriv…

Thm 1

A linear system has at least one solution if & only if the ri…

Thm 2

Let A be an mxn matrix coefficient matrix. Then the following…

Consistent System

Inconsistent System

Consistent Dependent System

Free variable

The matrix system has a solution

Matrix has no solution (last row 0 0 | non zero )

Infinite systems (last row 0 0 | 0 )

x1 x2 x3 etc can be any number, no set equation, no pivot in…

Consistent System

The matrix system has a solution

Inconsistent System

Matrix has no solution (last row 0 0 | non zero )

Equivalent Systems

consistent system

inconsistent system

Row Echelon Form Qualifications [REF]…

Have the same solution set

either one solution or infinitely many

no solution

1. All zero rows below nonzero rows... 2. Each leading entry of…

Equivalent Systems

Have the same solution set

consistent system

either one solution or infinitely many

basic variable

existance

consistent

inconsistant

variable that corresponds to a pivot column in the coefficien…

there is at least one solution to the matrix

the system of equations has at least one solution

the system has no solutions

basic variable

variable that corresponds to a pivot column in the coefficien…

existance

there is at least one solution to the matrix