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Introduction to Matrices- Introduction and Basic Operations
- Matrix Multiplication
- Algebraic Properties of Matrix Operations
- Invertible Matrices
- Special Matrices: Triangular, Symmetric, Diagonal
- Elementary Operations for Matrices
- Matrix Exponential
- Applications:
Systems of Linear Equations- System of Equations: An Introduction
- Systems of Linear Equations: Gaussian Elimination
- Systems of linear equations in Two variables.
- Systems of linear equations in Three variables.
- Application of Determinant to Systems: Cramer's Rule
- More Problems on Linear Systems and Matrices
Determinants- Introduction to Determinants
- Determinants of Matrices of Higher Order
- Determinant and Inverse of Matrices
- Application of Determinant to Systems: Cramer's Rule
Eigenvalues and Eigenvectors- Eigenvalues and Eigenvectors: An Introduction
- Computation of Eigenvalues
- Computation of Eigenvectors
- The Case of Complex Eigenvalues
- Diagonalization
APPENDIX
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