INSTRUCTORS Carleen Eaton Grant Fraser Professor Fraser

Matrix Operations

Slide Duration:

Section 1: Equations and Inequalities
Expressions and Formulas

28m 56s

Intro
0:00
Order of Operations
0:51
Variables and Algebraic Expressions
0:57
Order of Operations
3:05
Monomials
5:25
Examples
5:37
Constant, Coefficient, Degree, Power
6:27
Polynomials
8:29
Examples
8:42
Terms, Like Terms, Binomial, Trinomial
8:59
Formulas
12:35
Examples: Area, Volume, Surface Area
12:50
Lecture Example 1
15:50
Lecture Example 2
21:31
-1
-2
Properties of Real Numbers

23m 45s

Intro
0:00
Real Numbers
0:15
Rational Numbers
0:40
Irrational Numbers
1:38
Venn Diagram of the Real Numbers
2:55
Properties of Real Numbers
6:49
Commutative Property
7:06
Associative Property
7:27
Identity Property
8:01
Inverse Property
8:42
Distributive Property
10:05
Lecture Example 1
10:43
Lecture Example 2
13:08
-1
-2
Solving Equations

24m 41s

Intro
0:00
Translations
0:11
Example: Verbal to Algebraic Expressions
0:44
Properties of Equality
2:51
Reflexive, Symmetric, Transitive Properties
2:58
3:32
Solving Equations
6:09
Example
6:23
Solving for a Variable
8:49
Example: Surface Area of a Cone
8:58
Lecture Example 1
11:06
Lecture Example 2
12:39
-1
-2
Solving Absolute Value Equations

17m 36s

Intro
0:00
Absolute Value Expressions
0:10
Example: Positive Distance
0:15
Absolute Value Equations
1:07
Examples
1:18
No Solutions
2:54
Example: Empty Set
2:58
Number of Solutions
3:56
Examples
4:42
Lecture Example 1
6:42
Lecture Example 2
8:54
-1
-2
Solving Inequalities

19m 27s

Intro
0:00
Properties of Inequality
0:07
0:21
Subtraction Property
0:48
Example
1:02
Multiplication Properties
1:44
Multiplying by a Positive Number
1:48
Example: Positive
2:17
Multiplying by a Negative Number
2:25
Example: Negative
2:35
Division Properties
3:23
Example: Positive
3:32
Example: Negative
4:04
Describing the Solution Set
6:00
Set Builder Notation
6:15
Graphing
7:15
Lecture Example 1
8:04
Lecture Example 2
9:09
-1
-2
Solving Compound and Absolute Value Inequalities

24m 8s

Intro
0:00
Compound Inequalities
0:11
Example
0:33
'And' Inequality
3:41
Example: Set Intersection
4:00
'Or' Inequality
6:01
Example: Set Union
6:15
Absolute Value Inequalities
8:19
Examples
8:37
Lecture Example 1
11:43
Lecture Example 2
14:47
-1
-2
Section 2: Linear Relations and Functions
Relations and Functions

38m 15s

Intro
0:00
Coordinate Plane
0:38
0:44
Relations
4:08
Example: Ordered Pairs
4:14
Domain and Range
5:05
Functions
5:57
Example: Mapping
6:11
One-to-One Functions
9:58
Example
10:05
Graphs of Relations
13:42
Example: Discrete and Continuous
13:55
Vertical Line Test
16:26
Examples
16:38
Equations, Relations, Functions
19:38
Example: Independent and Dependent Variables
19:45
Function Notation
21:51
Examples
22:27
Lecture Example 1
24:39
Lecture Example 2
28:29
-1
-2
Linear Equations

12m 50s

Intro
0:00
Linear Equations and Functions
0:12
Example: Linear Equation
0:21
Example: Linear Function
1:16
Standard Form
2:13
Examples
2:43
Graphing with Intercepts
3:26
Example: Intercepts
3:51
Lecture Example 1
6:25
Lecture Example 2
7:53
-1
-2
Slope

20m 7s

Intro
0:00
Definition of Slope
0:23
Interpretation of Slope
2:19
Example: 0 Slope and Undefined Slope
2:25
Example: Positive Slope
4:04
Example: Negative Slope
4:43
Parallel Lines
6:16
Perpendicular Lines
7:15
Lecture Example 1
8:20
Lecture Example 2
10:45
-1
-2
Writing Linear Functions

27m 36s

Intro
0:00
Slope Intercept Form
0:08
Origin of Form
0:21
Example
2:08
Point Slope Form
3:47
Origin of Form
4:01
Parallel and Perpendicular Lines
5:36
Example: Find Parallel Line
5:58
Lecture Example 1
8:27
Lecture Example 2
12:08
-1
-2
Special Functions

24m 28s

Intro
0:00
Step Functions
0:13
Graph
0:21
Example: Birthday Function
2:32
Absolute Value Functions
5:21
Graph
5:27
Piecewise Functions
7:34
Example
7:38
Lecture Example 1
10:20
Lecture Example 2
14:38
-1
-2
Graphing Inequalities

30m 37s

Intro
0:00
Graphing Linear Inequalities
0:11
Example: Linear Inequalities
0:20
Half Plane
2:04
Test Point
2:53
Graphing Absolute Value Inequalities
5:38
Example: Linear Inequalities
5:49
Example: Absolute Value
8:23
Lecture Example 1
11:39
Lecture Example 2
14:50
-1
-2
Section 3: Systems of Equations and Inequalities
Solving Systems of Equations by Graphing

21m 27s

Intro
0:00
Systems of Equations
0:14
Solving by Graphing
0:34
Types of Systems
1:07
Independent (One Solution)
2:02
Dependent (Infinite Solutions)
2:30
Inconsistent (No Solutions, Parallel)
3:37
Lecture Example 1
4:52
Lecture Example 2
8:42
-1
-2
Solving Systems of Equations Algebraically

31m 26s

Intro
0:00
Solving by Substitution
0:15
Examples
0:50
Solving by Elimination
4:19
Examples
4:27
Solving by Multiplication
7:24
Examples
7:37
Inconsistent and Dependent Systems
11:42
Example: Spotting Differences
12:07
Lecture Example 1
15:00
Lecture Example 2
17:35
-1
-2
Solving Systems of Inequalities by Graphing

20m 43s

Intro
0:00
Solving by Graphing
0:10
Example: Single Inequality
0:14
No Solution
4:16
Example: No Solution
4:25
Lecture Example 1
6:25
Lecture Example 2
8:23
-1
-2
Solving Systems of Equations in 3 Variables

21m 27s

Intro
0:00
Solving Systems in Three Variables
0:15
Ordered Triple
0:36
Number of Solutions
1:32
Lecture Example 1
2:19
Lecture Example 2
6:14
-1
-2
Section 4: Matrices
Basic Matrix Concepts

14m 8s

Intro
0:00
What is a Matrix?
0:33
Example: Rectangular Array
0:41
Element
1:52
Examples: More Matrices
2:04
Dimensions
3:40
Examples
4:53
Special Matrices
6:31
(m x 1) Matrix
6:36
Square Matrix
7:01
Zero Matrix
7:38
Equal Matrices
8:23
Examples
8:32
Lecture Example 1
10:56
Lecture Example 2
11:28
-1
-2
Matrix Operations

16m 40s

Intro
0:00
0:10
Example
1:07
Matrix Subtraction
2:12
Example
2:31
Scalar Multiplication
3:23
Example
4:05
Properties of Matrix Operations
5:31
Commutative Property
5:48
Associative Property
5:59
Distributive Property
6:34
Lecture Example 1
7:03
Lecture Example 2
8:15
-1
-2
Matrix Multiplication

22m 47s

Intro
0:00
Dimension Requirement
0:19
Example
0:45
Matrix Multiplication
1:35
Example
2:21
Properties of Matrix Multiplication
6:46
Associative Property
6:59
Distributive Property
7:15
Commutative Property
7:39
Lecture Example 1
8:49
Lecture Example 2
11:43
-1
-2
Determinants

25m 47s

Intro
0:00
What is a Determinant
0:15
Determinant of a 2x2 Matrix
0:56
Difference from Matrices
1:16
Second Order Determinant
1:38
Example
2:06
Determinant of a 3x3 Matrix
3:20
Third Order Determinants
3:25
Origin of Equation (Minors)
3:38
Expansion by Minors
6:05
Example: 3x3 Matrix
8:55
Diagonal Method for 3x3 Matrix
12:45
Example
12:55
Lecture Example 1
17:03
Lecture Example 2
17:42
-1
-2
Cramer's Rule

25m 42s

Intro
0:00
System of 2 Equations in 2 Variables
0:27
Example
1:20
System of 3 Equations in 3 Variables
3:10
Example
3:51
Lecture Example 1
6:45
Lecture Example 2
10:22
-1
-2
Identity and Inverse Matrices

27m 1s

Intro
0:00
Identity Matrix
0:10
Example: 2x2 Matrix
2:18
Matrix Inverses
4:40
Example: Does Not Exist
6:04
Inverse of a 2x2 Matrix
8:17
Example
9:38
Lecture Example 1
13:19
Lecture Example 2
15:57
-1
-2
Solving Systems of Equations with Matrices

28m 40s

Intro
0:00
Matrix Equations
0:22
Example
0:40
Solving Systems of Equations
4:20
Example
5:58
Lecture Example 1
9:11
Lecture Example 2
15:09
-1
-2
Section 5: Quadratic Functions and Inequalities

26m 36s

Intro
0:00
0:10
Parabola
0:50
Example: Opens Upward
1:03
Example: Opens Downward
1:54
Properties of Parabolas
3:17
Axis of Symmetry
3:26
Vertex
4:05
Example
4:28
Maximum and Minimum Values
7:10
Example: Upwards/Minimum
7:32
Example: Downwards/Maximum
8:19
Lecture Example 1
9:09
Lecture Example 2
13:05
-1
-2

19m 26s

Intro
0:00
0:18
Example: Standard Form
0:55
Solving by Graphing
1:39
Roots
1:48
Example: 2 Solutions
1:56
Example: 1 Solution
2:39
Example: 0 Solutions
3:10
Estimating Solutions
3:55
Example
4:07
Lecture Example 1
5:16
Lecture Example 2
7:51
-1
-2

17m 46s

Intro
0:00
Factoring Techniques
0:16
Greatest Common Factor (GCF)
0:29
Difference of Two Squares
1:45
Perfect Square Trinomials
2:07
General Trinomials
3:16
Zero Product Rule
4:50
Example
5:01
Lecture Example 1
6:19
Lecture Example 2
8:13
-1
-2
Imaginary and Complex Numbers

37m 41s

Intro
0:00
Properties of Square Roots
0:17
Example: Product and Quotient Rules
0:33
Imaginary Numbers
4:04
Powers of Imaginary Numbers
5:06
Example
6:27
Complex Numbers
7:21
Real and Complex Numbers
8:19
Equality
9:04
Example
9:17
9:43
Example
9:55
Complex Plane
11:38
Example
11:52
Multiplication
13:34
Example
13:43
Division
16:36
Complex Conjugates
16:45
Example
18:16
Lecture Example 1
23:40
Lecture Example 2
26:34
-1
-2
Completing the Square

16m 42s

Intro
0:00
Square Root Property
0:22
Examples
0:33
Completing the Square
1:48
Example: Making into Perfect Square
1:50
Solve Equations
3:43
Example
3:53
Equations Where 'a' Not Equal to 1
6:47
Example
6:57
Complex Solutions
10:14
Example
10:22
Lecture Example 1
11:30
Lecture Example 2
12:34
-1
-2

17m 44s

Intro
0:00
0:37
Example
0:56
One Rational Root
3:10
Why It Works
3:26
Repeated/Double Root
3:49
Complex Solutions
4:31
Example
4:50
Discriminant
7:19
Discriminant Value and Root Type
8:50
Lecture Example 1
12:08
Lecture Example 2
14:15
-1
-2
Analyzing the Graphs of Quadratic Functions

23m

Intro
0:00
Vertex Form
0:24
Example
1:56
Significance of Coefficient 'a'
3:15
Example
3:39
Writing Quadratic Equations in Vertex Form
4:51
Examples
5:19
Lecture Example 1
8:14
Lecture Example 2
10:22
-1
-2

34m 38s

Intro
0:00
1:14
Example: Linear Inequality
1:29
3:11
6:32
Example
6:38
Lecture Example 1
11:50
Lecture Example 2
15:09
-1
-2
Section 6: Polynomial Functions
Properties of Exponents

20m 28s

Intro
0:00
Simplifying Exponential Expressions
0:32
Negative Exponents
0:54
Example: Base 0
1:16
Examples
1:30
Properties of Exponents
2:22
Base and Exponent
2:52
Lecture Example 1
8:29
Lecture Example 2
10:58
-1
-2
Operations on Polynomials

16m 13s

Intro
0:00
0:24
Example: Signs
0:34
Multiplying Polynomials
3:04
Example
3:12
Lecture Example 1
6:40
Lecture Example 2
7:21
-1
-2
Dividing Polynomials

29m 26s

Intro
0:00
Dividing by a Monomial
0:16
Example
0:28
Long Division
3:24
Example: Missing Terms, Remainder
3:49
Example: Long Division
6:51
Synthetic Division
10:13
Example
10:44
Divisor in Synthetic Division
13:18
Example: Coefficient Not 1
13:30
Lecture Example 1
16:41
Lecture Example 2
18:22
-1
-2
Polynomial Functions

29m 34s

Intro
0:00
Polynomial in One Variable
0:17
Degree n
0:30
Descending Order
0:43
1:04
Function Values
3:31
Example
3:42
Zeros of Polynomial Functions
5:45
Example: Zeros
6:04
End Behavior
9:51
Example: 4 Situations
10:51
Lecture Example 1
17:30
Lecture Example 2
19:11
-1
-2
Analyzing Graphs of Polynomials

34m 36s

Intro
0:00
Graphing Polynomial Functions
0:09
End Behavior
0:19
Examples: Degree and Sign of Polynomials
1:13
Location Principle
4:50
Example
6:19
Maximum and Minimum Points
7:34
Example: Relative Maximum and Relative Minimum
7:44
Lecture Example 1
10:17
Lecture Example 2
15:13
-1
-2
Solving Polynomial Equations

19m 23s

Intro
0:00
Factoring Polynomials
0:08
Example: Greatest Common Factor (GCF)
0:40
Example: Perfect Square Trinomials
1:30
Example: General Trinomials
2:48
Sum and Difference of Two Cubes
3:25
Example
4:18
6:20
Lecture Example 1
7:30
Lecture Example 2
10:43
-1
-2
Remainder and Factor Theorems

27m 52s

Intro
0:00
Remainder Theorem
0:04
Quotient and Remainder
0:30
Examples
1:34
Synthetic Substitution
5:04
Example
5:28
Factor Theorem
10:00
Factoring Polynomials
11:21
Example
11:51
Lecture Example 1
16:38
Lecture Example 2
18:41
-1
-2
Roots and Zeros

31m 4s

Intro
0:00
Numbers of Roots
0:10
Example: Real and Complex Roots
0:23
Descartes' Rule of Signs
3:43
Example: Positive Real Roots
4:58
Example: Negative Real Roots
8:00
Finding the Roots
12:11
Conjugate Roots
13:24
Lecture Example 1
15:41
Lecture Example 2
19:41
-1
-2
Rational Zero Theorem

29m 27s

Intro
0:00
Equation
0:14
0:30
Example
2:15
8:08
Example
9:20
Finding Rational Zeros
11:48
Lecture Example 1
12:10
Lecture Example 2
15:59
-1
-2
Section 7: Rational Equations and Inequalities
Operations on Functions

35m 12s

Intro
0:00
Arithmetic Operations
0:12
Example: Domain
0:25
Composition of Functions
7:35
Example
7:55
Composition is Not Commutative
17:13
Example
18:18
Lecture Example 1
21:51
Lecture Example 2
24:25
-1
-2
Inverse Functions and Relations

18m 12s

Intro
0:00
Inverse of a Relation
0:24
Example: Ordered Pairs
0:33
Inverse of a Function
2:15
Procedure to Construct an Inverse Function
4:28
Example: Inverse Function
4:58
Example: Inverse Function 2
7:31
Inverses and Compositions
8:41
Lecture Example 1
9:59
Lecture Example 2
10:45
-1
-2
Square Root Functions and Inequalities

26m 24s

Intro
0:00
Square Root Functions
0:06
Example: Not Square Root Function
0:23
Example: Square Root Function
1:17
Graphing Square Root Functions
3:11
3:21
Square Root Inequalities
6:51
Example
7:13
Lecture Example 1
11:27
Lecture Example 2
14:05
-1
-2
nth Roots

24m 6s

Intro
0:00
Definition of the nth Root
0:13
Example
0:36
Principal nth Root
2:18
Index
3:04
Examples
3:20
Using Absolute Values
6:25
Examples
6:52
Lecture Example 1
11:26
Lecture Example 2
13:17
-1
-2

34m 38s

Intro
0:00
0:22
Example
1:37
2:58
Examples
3:24
Rationalizing Denominators
4:08
Examples
4:18
8:01
Example
8:09
11:23
Examples
11:44
12:57
Examples
13:03
Lecture Example 1
16:53
Lecture Example 2
20:11
-1
-2
Rational Exponents

24m 36s

Intro
0:00
Definition 1
0:24
nth Root
0:44
Example: Even
1:29
Definition 2
2:55
Simplifying Expressions
3:20
Examples
3:40
Simplified Form
7:07
Example
7:32
Lecture Example 1
8:18
Lecture Example 2
10:20
-1
-2

38m 46s

Intro
0:00
0:23
Examples
0:34
4:47
Extraneous Roots
12:29
Eliminating nth Roots
14:28
Examples
14:54
16:38
Example
17:18
Lecture Example 1
20:28
Lecture Example 2
22:57
-1
-2
Section 8: Radical Expressions and Equations
Multiplying and Dividing Rational Expressions

30m 11s

Intro
0:00
Simplifying Rational Expressions
0:12
Examples: Rational Expressions
0:31
Factoring -1
3:26
Example
3:33
Multiplying and Dividing Rational Expressions
4:50
Multiplying
5:08
Dividing
5:16
Example
6:10
Factoring
9:13
Example
9:33
Complex Fractions
13:15
Example
13:27
Lecture Example 1
15:36
Lecture Example 2
18:25
-1
-2

51m 53s

Intro
0:00
Example: Fractions
0:22
Least Common Multiple (LCM)
1:36
Example
2:07
7:56
Least Common Denominator (LCD)
8:01
Example: Fractions
8:14
Example: Rational Expression
10:23
Equivalent Fractions
13:45
Example
14:20
Simplifying Complex Fractions
20:03
Example
20:28
Lecture Example 1
26:34
Lecture Example 2
31:06
-1
-2
Graphing Rational Functions

45m 13s

Intro
0:00
Rational Functions
0:35
Example
0:57
Breaks in Continuity
2:48
Discontinuities
3:19
Example: Excluded Values
3:52
Graphs and Discontinuities
4:36
Example: Hole Discontinuity
6:07
Example: Asymptote
8:53
Horizontal Asymptotes
13:34
Example
13:54
Lecture Example 1
17:58
Lecture Example 2
20:29
-1
-2
Direct, Joint, and Inverse Variation

21m 49s

Intro
0:00
Direct Variation
0:16
Constant of Variation
0:44
Graph of Direct Variation
1:28
Example: Straight Line
1:36
Joint Variation
2:55
Inverse Variation
4:17
Example
4:50
Graph of Inverse Variation
5:35
Example
6:00
Proportions
8:00
Example
9:28
Lecture Example 1
12:32
Lecture Example 2
14:26
-1
-2
Solving Rational Equations and Inequalities

53m 21s

Intro
0:00
Rational Equations
0:15
Example: Not Rational Equation
0:26
Example: X in Denominator
0:38
Example: LCD
1:08
Example: Rational Equations
5:19
Extraneous Solutions
12:08
Example
12:42
Rational Inequalities
15:31
Example
15:45
Example: Rational Inequalities
12:05
Lecture Example 1
32:06
Lecture Example 2
35:18
-1
-2
Section 9: Exponential and Logarithmic Relations
Exponential Functions

28m 22s

Intro
0:00
What is an Exponential Function?
0:11
Exponent and Base
0:38
Graphing Exponential Functions
1:31
Example
1:34
Properties
4:05
Growth and Decay
9:38
Equations
10:32
Example
11:05
Inequalities
13:00
Example
14:29
Lecture Example 1
16:48
Lecture Example 2
18:50
-1
-2
Logarithms and Logarithmic Functions

36m 31s

Intro
0:00
What are Logarithms?
0:17
Examples
1:30
Logarithmic Functions
4:09
Graph of the Logarithmic Function
4:52
Properties
9:08
Inverse Property
10:47
Equations
11:44
Example
12:11
Inequalities
14:45
Equations with Logarithms on Both Sides
17:00
Example
17:18
Inequalities with Logarithms on Both Sides
19:17
Example
19:32
Lecture Example 1
20:31
Lecture Example 2
22:38
-1
-2
Properties of Logarithms

29m 50s

Intro
0:00
Product Property
0:08
Example
0:26
Quotient Property
1:06
Example
1:12
Power Rule
3:29
Example
3:33
Equations
5:43
Example
6:19
Lecture Example 1
12:19
Lecture Example 2
16:13
-1
-2
Common Logarithms

27m 10s

Intro
0:00
What are Common Logarithms?
0:54
Base 10
0:58
Equations
2:00
Examples
2:22
Inequalities
5:35
Example
5:42
Change of Base
9:23
Example
10:09
Lecture Example 1
12:04
Lecture Example 2
15:16
-1
-2
Base 'e' and Natural Logarithms

19m 52s

Intro
0:00
The Number 'e'
0:32
Natural Base
0:44
Euler
1:12
Natural Exponential Function
1:38
Natural Log Function
2:44
Growth and Decay
2:55
Natural Logarithms
3:16
Graph (Inverse)
3:34
Equations and Inequalities
4:49
Lecture Example 1
7:21
Lecture Example 2
9:10
-1
-2
Exponential Growth and Decay

28m 10s

Intro
0:00
Decay
0:15
Fixed Percentage
0:24
Rate of Decay
2:35
Scientific Model of Decay (Exponential Decay)
4:17
Graph
5:19
Growth
6:19
Rate of Growth
6:36
Scientific Model of Growth (Exponential Growth)
6:41
Graph
6:48
Lecture Example 1
7:48
-1
-2
Section 10: Conic Sections
Midpoint and Distance Formulas

29m 35s

Intro
0:00
Midpoint Formula
0:35
Distance Formula
1:42
Example
2:52
Lecture Example 1
3:40
Lecture Example 2
6:37
-1
-2
Parabolas

26m 11s

Intro
0:00
What is a Parabola?
0:21
Focus and Directrix
0:33
Axis of Symmetry
1:41
Vertex
2:03
Example
2:15
Standard Form
3:11
Upward and Downward
4:07
Graphing Parabolas
5:24
Example
6:32
Latus Rectum
7:37
Horizontal Parabolas
9:10
Focus and Direction
12:31
Lecture Example 1
13:11
Lecture Example 2
16:46
-1
-2
Circles

17m 33s

Intro
0:00
What are Circles
0:17
0:37
Equation (Standard Form)
0:46
Graphing
1:21
Center Not at Origin
1:53
Example
2:06
Lecture Example 1
4:16
Lecture Example 2
8:22
-1
-2
Ellipses

38m 57s

Intro
0:00
What are Ellipses?
0:59
Foci
1:04
Properties
3:47
Major Axis, Minor Axis
4:03
Standard Form
7:22
Example
8:05
Vertical Major Axis
10:12
Example
10:40
Graphing Ellipses
13:33
Example: Completing the Square
14:04
Equation with Center at (h,k)
17:25
Example
17:53
Lecture Example 1
19:36
Lecture Example 2
23:52
-1
-2
Hyperbolas

37m 59s

Intro
0:00
What are Hyperbolas?
1:09
Properties
2:35
Transverse Axis, Conjugate Axis
2:57
Center, Vertices
3:54
Standard Form
4:33
Vertical Transverse Axis
6:35
Asymptotes
10:17
Graphing Hyperbolas
13:44
Example
17:23
Equation with Center at (h,k)
18:20
Lecture Example 1
20:19
Lecture Example 2
23:25
-1
-2
Conic Sections

23m 10s

Intro
0:00
What are Conic Sections?
2:16
Standard Form
2:58
Example
5:29
Identifying Conic Sections
6:14
Example
6:55
Lecture Example 1
8:55
Lecture Example 2
11:18
-1
-2

28m 18s

Intro
0:00
0:04
Example
0:28
Solutions
3:13
3:36
Example: Elimination
3:45
Solutions
7:34
7:55
Example
8:07
Lecture Example 1
11:10
Lecture Example 2
16:12
-1
-2
Section 11: Sequences and Series
Arithmetic Sequences

27m 44s

Intro
0:00
Sequences
0:27
Example: Term
0:36
Arithmetic Sequence
2:13
Common Difference
2:22
Example
2:35
Formula for nth Term
3:39
Example
4:29
Equation for nth Term
5:58
Example
6:10
Arithmetic Means
7:40
Example
8:13
Lecture Example 1
14:08
Lecture Example 2
15:35
-1
-2
Arithmetic Series

29m 12s

Intro
0:00
What are Arithmetic Series?
0:22
Example: Sequence
0:29
Example: Common Difference (d)
0:35
Sum of Arithmetic Series
2:52
Example
3:44
Sigma Notation
6:10
Example
6:48
Lecture Example 1
8:32
Lecture Example 2
12:39
-1
-2
Geometric Sequences

24m 52s

Intro
0:00
What are Geometric Sequences?
0:20
Common Ratio
1:03
Example
1:20
nth Term of a Geometric Sequence
3:39
Geometric Means
4:16
Example: Missing Term
5:06
Lecture Example 1
8:09
Lecture Example 2
11:42
-1
-2
Geometric Series

27m 2s

Intro
0:00
What are Geometric Series?
0:20
Example: Common Ratio
1:00
Sum of Geometric Series
2:27
Example
4:01
Sigma Notation
4:56
Example: Index
5:24
Example
6:20
Another Sum Formula
7:51
Specific Terms
9:19
Lecture Example 1
11:15
Lecture Example 2
14:30
-1
-2
Infinite Geometric Series

24m 1s

Intro
0:00
What are Infinite Geometric Series?
0:35
Partial Sums of the Infinite Series
1:17
Example
1:24
Sum of an Infinite Geometric Series
3:16
Convergent Series
3:25
Example
4:17
Sigma Notation
5:31
Example
5:43
Repeating Decimals
6:38
Example
6:48
Lecture Example 1
9:33
Lecture Example 2
11:20
-1
-2
Recursion and Special Sequences

17m 11s

Intro
0:00
Fibonacci Sequence
0:17
Example: Fibonacci Sequence
0:36
Example: Recursive Formula
2:38
Iteration
3:40
Example
4:57
Lecture Example 1
7:10
Lecture Example 2
9:03
-1
-2
Binomial Theorem

38m 25s

Intro
0:00
Pascal's Triangle
0:11
General Form
2:43
Properties
7:01
Binomial Theorem
9:20
Example
11:47
Finding a Specific Term
16:24
Example
16:32
Lecture Example 1
20:35
Lecture Example 2
23:30
-1
-2
Proof and Mathematical Induction

19m 53s

Intro
0:00
Math Induction Principle
0:19
Example
0:29
Counter Examples
5:00
Example
5:14
Lecture Example 1
7:16
Lecture Example 2
10:53
-1
-2
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• ## Related Books 1 answerLast reply by: Arshin jainFri Aug 3, 2012 6:09 PMPost by michael egler on February 17, 2010in ex 1 - - - - - - is called 2x3 matrixin ex 4 - - - - - - is called 2x3 as wellis this correct? thanks in advance!

### Matrix Operations

• Matrices can be added or subtracted if and only if they have the same dimensions.

• Matrix addition is commutative and associative

• Scalar multiplication satisfies the distributive property.

### Matrix Operations

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• Intro 0:00
• Example
• Matrix Subtraction 2:12
• Example
• Scalar Multiplication 3:23
• Example
• Properties of Matrix Operations 5:31
• Commutative Property
• Associative Property
• Distributive Property
• Lecture Example 1 7:03
• Lecture Example 2 8:15

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### Start Learning Now

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