Precalculus

  1. Systems of Equations and Matrices
    1. Systems of Linear Equations
      1. Systems in Two Variables
        1. Graphical Method
          1. Substitution Method
            1. Elimination Method
            2. Systems in Three Variables
              1. Substitution Method
                1. Elimination Method
                  1. Geometric Interpretation
                  2. Types of Solutions
                    1. Unique Solution
                      1. No Solution (Inconsistent)
                        1. Infinitely Many Solutions (Dependent)
                        2. Applications of Systems
                          1. Mixture Problems
                            1. Motion Problems
                              1. Investment Problems
                            2. Matrices and Systems
                              1. Matrix Notation
                                1. Rows and Columns
                                  1. Dimensions
                                    1. Elements
                                    2. Augmented Matrices
                                      1. Coefficient Matrix
                                        1. Constant Vector
                                        2. Elementary Row Operations
                                          1. Row Interchange
                                            1. Row Multiplication
                                              1. Row Addition
                                              2. Row-Echelon Form
                                                1. Leading Entries
                                                  1. Zero Rows
                                                  2. Reduced Row-Echelon Form
                                                    1. Gaussian Elimination
                                                      1. Gauss-Jordan Elimination
                                                        1. Back-Substitution
                                                        2. Matrix Operations
                                                          1. Matrix Addition and Subtraction
                                                            1. Same Dimensions Requirement
                                                              1. Element-wise Operations
                                                              2. Scalar Multiplication
                                                                1. Matrix Multiplication
                                                                  1. Dot Product Method
                                                                    1. Dimensions Compatibility
                                                                      1. Non-commutative Property
                                                                      2. Properties of Matrix Operations
                                                                        1. Associative Property
                                                                          1. Distributive Property
                                                                            1. Identity Matrix
                                                                            2. Transpose of a Matrix
                                                                            3. Inverse Matrices
                                                                              1. Definition of Inverse Matrix
                                                                                1. Properties of Inverse Matrices
                                                                                  1. Finding Inverse of 2×2 Matrix
                                                                                    1. Finding Inverse Using Gauss-Jordan Method
                                                                                      1. Solving Systems Using Inverse Matrices
                                                                                        1. Conditions for Invertibility
                                                                                        2. Determinants
                                                                                          1. Determinant of 2×2 Matrix
                                                                                            1. Determinant of 3×3 Matrix
                                                                                              1. Cofactor Expansion
                                                                                                1. Rule of Sarrus
                                                                                                2. Properties of Determinants
                                                                                                  1. Effect of Row Operations
                                                                                                    1. Determinant of Product
                                                                                                      1. Determinant of Inverse
                                                                                                      2. Cramer's Rule
                                                                                                        1. Systems with Unique Solutions
                                                                                                        2. Applications of Determinants
                                                                                                          1. Area of Triangle
                                                                                                            1. Volume of Parallelepiped

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                                                                                                        8. Polar Coordinates and Complex Numbers

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                                                                                                        10. Sequences, Series, and Mathematical Induction