Midterm
1. System of Linear Equations and Matrices
- System of Linear Equations
- Elementary Operations
- Elimination Methods
- Matrices and Matrix Operations
- Inverses ; Rules of Matrix Arithmetic
- Elementary Matrices and a Method
2. Determinants
- Determinants by Cofactor Expansion
- Inverse of a Matrix Using Its Adjoint
- Cramer's Rule
- Evaluating Determinants by Row Reduction
- Properties of Determinants
3. Vector Spaces
- Definition and Examples
- Subspaces
- Spanning Set and Linear Independence
1. System of Linear Equations and Matrices
- System of Linear Equations
- Elementary Operations
- Elimination Methods
- Matrices and Matrix Operations
- Inverses ; Rules of Matrix Arithmetic
- Elementary Matrices and a Method
2. Determinants
- Determinants by Cofactor Expansion
- Inverse of a Matrix Using Its Adjoint
- Cramer's Rule
- Evaluating Determinants by Row Reduction
- Properties of Determinants
3. Vector Spaces
- Definition and Examples
- Subspaces
- Spanning Set and Linear Independence
1. Basis and Dimension
2. Row Space, Column Space, and Null Space
3. Rank and Nullity
4. Linear Transformations
- Definition and Examples
- Kernel and Range
- Matrix Representations of Linear Transformations
5. Eigenvalues, Eigenvectors
- Eigenvalues, Eigenvectors
- Diagonalization
6. Inner Product Spaces
- Inner Products
- Angle and Orthogonality in Inner Product Spaces
- Least Squares Problems
- Orthogonal Matrix
- Complex Inner Product
- Fundamentals Concepts of Tensor
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