Table of Contents
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Algebra: Matrices
- Introduction to Matrices
- Types of Matrices
- Equal Matrices
- Scalar Multiplication of Matrices
- Transpose of a Matrix
- Adding and Subtracting Matrices
- Matrix Operations
- Matrix Multiplication
- Properties of Matrix Multiplication
- Power of a Matrix
- Two-by-Two Determinants
- Three-by-Three Determinants
- Determinant of a Triangular Matrix
- Using Determinants to Calculate Areas
- Cramer’s Rule
- Inverse of a 2 × 2 Matrix
- Representing a System of Two Equations in Matrix Form
- Solving a System of Two Equations Using a Matrix Inverse
- Algebra: Linear Programing
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Analytic Geometry: Vectors
- Scalars, Vectors, and Directed Line Segments
- Components of a Vector
- Magnitude of a 2D Vector
- Adding and Subtracting Vectors in 2D
- Properties of Operations on Vectors
- Vectors in terms of Fundamental Unit Vectors
- Polar Form of a Vector
- Parallel and Perpendicular Vectors in 2D
- Vector Operations in 2D
- Graphical Operations on Vectors
- Geometric Applications of Vectors
- Vector Applications
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Analytic Geometry: Straight Lines
- Partitioning a Line Segment on the Coordinate Plane
- Equation of a Straight Line: Vector Form
- Equation of a Straight Line: Parametric Form
- Equation of a Straight Line: General Form
- Equation of a Straight Line: Two-Intercept Form
- Angle between Two Straight Lines in the Coordinate Plane
- Perpendicular Distance from a Point to a Line on the Coordinate Plane
- Intersection Point of Two Straight Lines on the Coordinate Plane
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Trigonometry
- Simplifying Trigonometric Expressions
- Simplifying Trigonometric Expressions Using Trigonometric Identities
- Evaluating Trigonometric Functions Using Pythagorean Identities
- Simple Trigonometric Equations
- Solving a Trigonometric Equation
- Right Triangle Trigonometry: Solving for a Side
- Right Triangle Trigonometry: Solving for an Angle
- Angles of Elevation and Depression
- Areas of Circular Sectors
- Areas of Circular Segments
- Finding the Area of a Triangle Using Trigonometry
- Areas of Regular Polygons