Linear Algebra

  1. Determinants
    1. Definition and Computation
      1. Determinant of 2×2 matrices
        1. Determinant of 3×3 matrices
          1. Minors and cofactors
            1. Cofactor expansion
              1. Recursive definition for n×n matrices
              2. Properties of Determinants
                1. Determinants of triangular matrices
                  1. Effects of elementary row operations
                    1. Row interchange
                      1. Row scaling
                        1. Row addition
                        2. Determinant of matrix products
                          1. Determinant of transpose
                            1. Determinant of inverse matrices
                              1. Zero determinant conditions
                              2. Applications of Determinants
                                1. Matrix invertibility criterion
                                  1. Adjugate matrix
                                    1. Computing inverses using determinants
                                      1. Cramer's rule
                                        1. Statement and application
                                          1. Limitations and computational considerations
                                          2. Geometric interpretations
                                            1. Area in R²
                                              1. Volume in R³
                                                1. Orientation and signed measures

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                                            2. Matrix Theory and Operations

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                                            4. Vector Spaces and Subspaces