Contents

1. Matrices
1. Matrix Operations
2. Elementary Matrices, Elementary Row Operations
3. Row Reduction and Echelon Forms
4. LU Factorization of Matrix
2. Determinants
1. Introduction to Determinants
2. Properties of Determinants
3. Determinant by Row Reduction
4. Determinant by Cofactor Expansion along any Row or Column
3. Invertible Matrices
1. The Inverse of a Matrix
2. Characterization of Invertible Matrices
3. To Find Inverse of a Matrix By Row Reduction
4. To find the Inverse of a Matrix by Adjoint Method
4. Linear Equations
1. Introduction
2. System of Linear Equations
3. The Matrix Equation Ax = b
4. Gauss Elimination Method
5. Cramer's Rule
6. Application of LU-Decomposition to Solve System Ax = b