Introduction | 1 | Elementary Linear Algebra and its Application | 1-5 |

Introduction to Matrices. | 2 | (3rd edition) | 6-17 |

System Of Linear Equations. | 3 | By David C. Lay | 18-29 |

Row reduction and Echelon Form of a Matrix. | 4 | | 30-43 |

Vector Equations. | 5 | | 44-55 |

Matrix Equations. | 6 | | 56-65 |

Solution Set of Linear Equations. | 7 | | 66-73 |

Linearly Dependent and Linearly Independent Sets. | 8 | | 81-88 |

Linear Transformations. | 9 | | 89-225 |

The Matrix of Linear Transformations. | 10 | | 98-107 |

Matrix Algebra. | 11 | | 121-133 |

Inverse of a Matrix. | 12 | | 134-143 |

Characterization of Invertible Matrices. | 13 | | 144-149 |

Partitioning of a Matrix. | 14 | | 150-157 |

Matrix Factorization. | 15 | | 158-167 |

Iterative Solution of Linear Systems. | 16 | | 168-201 |

Introduction to Determinants. | 17 | | 202-207 |

Properties of Determinants. | 18 | | 208-216 |

Cramer"s rule, Volume and Linear Transformations. | 19 | | 217-222 |

Vector Spaces. | 20 | | 232-241 |

Null Spaces, Column Spaces and Linear Transformations. | 21 | | 242-252 |

Bases for a vector Space. | 22 | | 253-261 |

Coordinate systems. | 23 | | 262-271 |

Dimension of a Vector Space. | 24 | | 272-278 |

The Rank Theorem and Invertible Matrix Theorem. | 25 | | 278-286 |

Change of Bases of a Vector Space. | 26 | | 287-289 |

Applications of vector spaces to Difference Equations. | 27 | | 290-301 |

Eigenvalues of a Matrix. | 28 | | 317-325 |

Characteristic Equation of a Matrix. | 29 | | 326-334 |

Diagonalization of a Matrix. | 30 | | 335-343 |

Eigen Vectors of linear Transformation. | 31 | | 343-350 |

Complex Eigenvalues and Vectors. | 32 | | 351-358 |

Discrete Dynamical Systems. | 33 | | 358-364 |

Applications to Differential Equations. | 34 | | 369-373 |

Iterative Estimates for Eigenvalues. | 35 | | 379-384 |

Revision | 36 | | 385-386 |

Revision (system of Linear Equations). | 37 | | 386-387 |

Inner Product and orthogonal vectors. | 38 | | 387-399 |

Orthogonal Sets. | 39 | | 400-402 |

Orthogonal Projections. | 40 | | 402-407 |

Null Spaces, Column Spaces and Linear Transformations. | 41 | | 413-417 |

Gram-Schmidt Process for finding orthogonal Bases of a Vector Space. | 42 | | 418-423 |

Inner Product Spaces. | 43 | | 443-450 |

Applications of Inner Product Spaces. | 44 | | 452-454 |

Revision of the Course and Vector Spaces. | 45 | | 455-458 |