College Algebra

  1. Matrices and Determinants
    1. Introduction to Matrices
      1. Definition and Notation
        1. Dimensions of Matrices
          1. Types of Matrices
            1. Square Matrices
              1. Row Matrices
                1. Column Matrices
                  1. Zero Matrices
                    1. Identity Matrices
                  2. Matrix Operations
                    1. Matrix Equality
                      1. Matrix Addition and Subtraction
                        1. Scalar Multiplication
                          1. Matrix Multiplication
                            1. Conditions for Multiplication
                              1. Process and Algorithm
                              2. Applications of Matrix Operations
                              3. Solving Linear Systems with Matrices
                                1. Augmented Matrices
                                  1. Row Operations
                                    1. Row Echelon Form
                                      1. Reduced Row Echelon Form
                                        1. Gauss-Jordan Elimination
                                          1. Interpreting Solutions
                                          2. Determinants
                                            1. Determinant of 2×2 Matrices
                                              1. Determinant of 3×3 Matrices
                                                1. Cofactor Expansion
                                                  1. Rule of Sarrus
                                                  2. Properties of Determinants
                                                    1. Applications of Determinants
                                                    2. Matrix Inverses
                                                      1. Definition and Properties
                                                        1. Finding Inverses of 2×2 Matrices
                                                          1. Using Inverses to Solve Systems
                                                            1. When Inverses Don't Exist
                                                            2. Cramer's Rule
                                                              1. Statement of the Rule
                                                                1. Applying Cramer's Rule
                                                                  1. When Cramer's Rule Applies
                                                                    1. Advantages and Limitations

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                                                                  6. Systems of Equations and Inequalities

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                                                                  8. Sequences, Series, and the Binomial Theorem