Solving Systems of Equations by Graphing
Parametric Representation of the Solution Set to a Linear Equation
Determining the Intersection of Two Graph on the TI83/84
Ex: Identify the Solution to a System of Equation Given a Graph, Then Verify
Ex 1: Solve a System of Equations by Graphing
Ex 2: Solve a System of Equations by Graphing
Ex: Solve a System of Equations by Graphing (Infinite Solutions)
Ex: Solve a System of Equations by Graphing (No Solution)
Regression and Systems of Equations: Application
Solving Systems of Equations Using Substitution
Solving Systems of Equations by Substitution
Ex 1: Solve a System of Equations Using Substitution
Ex 2: Solve a System of Equations Using Substitution
Ex 3: Solve a System of Equations Using Substitution
Ex 4: Solve a System of Equations Using Substitution
Ex: Solve a System of Equations Using Substitution - Infinite Solutions
Ex: Solve a System of Equations Using Substitution - No Solution
Solving Systems of Equations Using Elimination
Solving Systems of Equations by Elimination
Ex 1: Solve a System of Equations Using the Elimination Method
Ex 2: Solve a System of Equations Using the Elimination Method
Ex 3: Solve a System of Equations Using the Elimination Method
Ex: System of Equations Using Elimination (Infinite Solutions)
Ex: System of Equations Using Elimination (No Solution)
Applications of Systems of Equations
Applications Involving Systems of Equations
More Applications Involving Systems of Equations
Ex: System of Equations Application - Number Problem Using Substitution
Ex: System of Equations Application - Number Problem Using Elimination
Ex: System of Equations Application - Compare Phone Plans
Ex: System of Equations Application - Entrance Fees
Ex: System of Equations Application - Coin Problem
Ex: System of Equations Application - Plane and Wind Problem
Ex: System of Equations Application - Commission and Salary
Ex: System of Equations Application - Investment Accounts
Ex: System of Equations Application (Corral Perimeter)
Ex: System of Equations Application - Mixture Problem
Systems of Equations with Three Unknowns
System of Equations in Three Variables: Part 1, Part 2
Ex 1: System of Three Equations with Three Unknowns Using Elimination
Ex 2: System of Three Equations with Three Unknowns Using Elimination
Ex 3: System of Three Equations with Three Unknowns Using Elimination (Fractions)
Ex 4: System of Three Equations with Three Unknowns Using Elimination (No Solution)
Ex 5: System of Three Equations with Three Unknowns Using Elimination (Infinite Solutions)
Matrices
Dimensions of a Matrix
Introduction to Augmented Matrices
Diagonal Matrices
Transpose of a Matrix
Echelon Form, Pivots, and Free Variables
Augmented Matrices
Augmented Matrices: Row Echelon Form
Ex 1: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 2: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 3: Solve a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 1: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 2: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Ex 3: Solve a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
Augmented Matrices: Reduced Row Echelon Form
Ex 1: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex 2: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex 3: Solve a System of Two Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Ex: Solve a System of Three Equations Using an Augmented Matrix (Reduced Row Echelon Form)
Augmented Matrices on the Graphing Calculator
Use Elementary Matrices to Perform Row Operations to Solve a System
Write a Matrix as a Product of Elementary Matrices
Matrix OperationsUse Elementary Matrices to Perform Row Operations to Solve a SystemWrite a Matrix as a Product of Elementary MatricesMatrix Addition, Subtraction and Scalar MultiplicationEx: Matrix Addition and SubtractionEx: Matrix Scalar MultiplicationEx: Matrix Operations - Scalar Multiplication, Addition, and SubtractionEx: Matrix Addition Application - TranslationEx: Matrix Scalar Multiplication Application - DilationMatrix MultiplicationMatrix Multiplication on the Graphing CalculatorEx 1: Matrix Multiplication (Basic)Ex 2: Matrix Multiplication (2x3)*(3x2)Ex 3: Matrix Multiplication (3x2)*(2x3)Ex Applicaton of Matrix Multiplication - TransformationAnimation: Matrix MultiplicationThe Identity MatrixElementary MatricesLU Decomposition Using Elementary MatricesLU Decomposition - Shortcut
Matrix Operations
Matrix Addition, Subtraction and Scalar Multiplication
Ex: Matrix Addition and Subtraction
Ex: Matrix Scalar Multiplication
Ex: Matrix Operations - Scalar Multiplication, Addition, and Subtraction
Ex: Matrix Addition Application - Translation
Ex: Matrix Scalar Multiplication Application - Dilation
Matrix Multiplication
Matrix Multiplication on the Graphing Calculator
Ex 1: Matrix Multiplication (Basic)
Ex 2: Matrix Multiplication (2x3)*(3x2)
Ex 3: Matrix Multiplication (3x2)*(2x3)
Ex Applicaton of Matrix Multiplication - Transformation
Animation: Matrix Multiplication
The Identity Matrix
Elementary Matrices
LU Decomposition Using Elementary Matrices
LU Decomposition - Shortcut
Inverse Matrices
2 x 2 Inverse Matrix Formula
Inverse Matrices Using Augmented Matrices
Ex: Find the Inverse of a 2x2 Matrix Using a Formula
Ex: Inverse of a 2x2 Matrix Using an Augmented Matrix
Ex 1: Inverse of a 3x3 Matrix Using an Augmented Matrix
Ex 2: Inverse of a 3x3 Matrix Using an Augmented Matrix
Inverse Matrices on the Graphing Calculator
Matrix Equations
Ex 1: Solve a System of Two Equations Using a Matrix Equation
Ex 2: Solve a System of Two Equations Using a Matrix Equation
Ex: Solve a System of Three Equations Using a Matrix Equation
Solve a System of Linear Equations Using LU Decomposition
Perform Linear Regression Using Matrices
Determinants
Ex: Determinant of a 2x2 Matrix
Ex 1: Determinant of 3x3 Matrix - Diagonal Method
Ex 2: Determinant of 3x3 Matrix - Diagonal Method
Ex 1: Determinant of 3x3 Matrix - Cofactor Method
Ex 2: Determinant of 3x3 Matrix - Cofactor Method
Determinants on the Graphing Calculator
Cramer’s Rule
Ex: Solve a System of Two Equations Using Cramer's Rule
Ex: Solve a System of Three Equations Using Cramer's Rule
Area Using Determinants
Vectors
Introduction to Vectors
Vector Operations
Unit Vector
Find the Component Form of a Vector from the Graph of a Vector
Ex: Find the Direction and Magnitude of a Vector in Component Form
Find the Component Form of a Vector Given Magnitude and Direction
Ex: Write a Vector as a Combination of Two Vectors
Ex: Find the Net Force of Three Vectors and the Opposite Force
Ex: Find the Coordinates of a Rotated Point Using Vectors
Ex: Direction and Speed of a Plane in the Wind Using Vectors
Applications of Vectors
Determining the Angle Between Two Vectors
Proof of the formula for the Angle Between Two Vectors
Vector Projection
Proof of the Vector Projection Formula
Vector Applications: Force and Work
Vectors in Space
Plotting Points in 3D
The Equation of a Sphere
Parallel Vectors
Vector Cross Products
An Application of Cross Products: Torque
The Triple Scalar Product: Volume of a Parallelepiped
Parametric Equations of Lines in 3D
The Equation of a Plane in 3D Using Vectors
Graphing a Plane in 3D
Determining the Angle Between Two Planes
Determining the Distance Between a Plane and a Point
Determining the Distance Between a Line and a Point
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