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

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

linear equation

slope

y-intercept

x-intercept

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

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

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

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

linear equation

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

slope

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

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

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.

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 the…

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

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

An equation whose graph is a line.

Quadrant

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

Solution of an equation in two variables

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

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

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. T…

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. T…

Matrix equation

Theorem 3

Identity matrix

Theorem 4

an equation that involves at least one matrix for instance, Ax…

If A is an m*n matrix, with columns a1...an, and if b is in Rm…

A square matrix with ones on the diagonal and zeros elsewhere

Let A be an m*n matrix. Then the following statements are logi…

Matrix equation

an equation that involves at least one matrix for instance, Ax…

Theorem 3

If A is an m*n matrix, with columns a1...an, and if b is in Rm…

Augmented Matrix

3x4 Matrix

Elementary Row Operations for Matrices

Row Equivalent Matrices

3 rows and 4 columns

(1) Interchange any two rows... (2) Multiply a row by any nonzero…

Matrices that have a sequence of row operations to transform o…

Augmented Matrix

3x4 Matrix

3 rows and 4 columns

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 a…

Equivalent Systems

Have the same solution set

consistent system

either one solution or infinitely many

linear equation

slope

y-intercept

x-intercept

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

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

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

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

linear equation

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

slope

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

Slope

Y-intercept

Standard Form

Slope-intercept Form

(y₂-y₁)/(x₂-x₁)

The point where the graph crosses the y-axis. In a linear equa…

Ax + By=C, where A, B, and C are not decimals or fractions, wh…

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

Slope

(y₂-y₁)/(x₂-x₁)

Y-intercept

The point where the graph crosses the y-axis. In a linear equa…

X-Intercept

Y-Intercept

Linear Function

Rate

The x-coordinate(s) of the point(s) where a graph intersects t…

The y-coordinate(s) of the point(s) where a graph intersects t…

A function that can be written in the form y=mx+b, where x is…

A ratio that compares two quantities measured in different uni…

X-Intercept

The x-coordinate(s) of the point(s) where a graph intersects t…

Y-Intercept

The y-coordinate(s) of the point(s) where a graph intersects t…

linear equation

slope

Types of Slope

y-intercept

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

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

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

linear equation

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

slope

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

linear equation

slope

y-intercept

x-intercept

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

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

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

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

linear equation

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

slope

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

solution

Gauss-Jordan elimination

elementary transformations

Echelon system

pair of x and y values that satisfies all equations in a syste…

1) put in augmented matrix form... 2) make triangle of zeros on b…

interchanging equations, multiplying a row by a nonzero consta…

3 zeros in the lower left hand corner

solution

pair of x and y values that satisfies all equations in a syste…

Gauss-Jordan elimination

1) put in augmented matrix form... 2) make triangle of zeros on b…

Linear Equation

Linear Equation Solution

Solution Set

Free Variable

an equation that can be written in the form a1b1+a2x2+...+anxn…

a list of numbers that makes that equation true

The set of all possible solutions for an equation. Described u…

y=8-2x (x is the free variable)... it can take on any real number…

Linear Equation

an equation that can be written in the form a1b1+a2x2+...+anxn…

Linear Equation Solution

a list of numbers that makes that equation true

Linear Equation

Linear Coefficients

System of linear equations (linear syst…

Solution of a linear system

1. variables x1......xn that can be written in the form:... a1x1…

Can be real or complex numbers

Collection of one of more linear equations that contain x1....…

List (s1, s2.....,sn) of numbers that makes each equation a tr…

Linear Equation

1. variables x1......xn that can be written in the form:... a1x1…

Linear Coefficients

Can be real or complex numbers