# Study sets matching "1 linear algebra"

Study sets

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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…

Algebraically, the value of the output when the input is zero…

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…

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

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…

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

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…

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.

Homogeneous Linear System

Trivial/Nontrivial Solutions

The homogeneous equation Ax=0 has a non…

A nontrivial solution x can have some z…

1. A system of linear equations is said to be homogeneous if i…

1. The zero solution is called the trivial solution... 2. The non…

the equation has at least one free variable.

not all of the entries are zero.

Homogeneous Linear System

1. A system of linear equations is said to be homogeneous if i…

Trivial/Nontrivial Solutions

1. The zero solution is called the trivial solution... 2. The non…

rate or rate of change

constant rate of change

constant rate of change

zero rate

measure like miles per hour or price per item

rate that stays the same throughout the table

graph of this rate is a straight line

graph of this rate is a horizontal line

rate or rate of change

measure like miles per hour or price per item

constant rate of change

rate that stays the same throughout the table

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…

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

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

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

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.

Theorem #2: If A is a triangular matrix…

An n x n determinant is defined by dete…

The (i, j) cofactor of a matrix A is th…

The cofactor expansion of det A down a…

The product of all main diagonal elements

True

False

?

Theorem #2: If A is a triangular matrix…

The product of all main diagonal elements

An n x n determinant is defined by dete…

True

If A and B are 3 x 3 and B = [b1 b2 b3]…

The second row of AB is the second row…

(AB)C = (AC) B

(Ab)^t = A^tB^t

False, because AB= [Ab1 Ab2 Ab3] the columns of the product ar…

True

True

true

If A and B are 3 x 3 and B = [b1 b2 b3]…

False, because AB= [Ab1 Ab2 Ab3] the columns of the product ar…

The second row of AB is the second row…

True