Linear
Algebra MATH 147
Assisted:
Dr. Daniel Reich
Dr. Maria Lorenz
Dr. Orin Chein
1.
Systems of Linear Equations.
2. Row
Reduction and Echelon Forms.
3.
Vector Equations.
4. The
Matrix Equation Ax = b.
5.
Solution Sets of Linear Systems.
6.
Linear Independence.
7.
Introduction to Linear Transformations.
8. The
Matrix of a Linear Transformation.
Chapter 2: Matrix Algebra
1.
Matrix Operations.
2. The
Inverse of a Matrix.
3.
Characterizations of Invertible Matrices.
9.
Subspaces of Rn.
Chapter 3: Determinants
1.
Introduction to Determinants.
2.
Properties of Determinants.
Chapter 4: Vector Spaces
1.
Vector Spaces and Subspaces.
2.
Null Spaces, Column Spaces, and Linear Transformations.
3.
Linearly Independent Sets; Bases.
4.
Coordinate Systems
5. The
Dimension of a Vector Space.
6.
Rank.
7.
Change of Basis
Chapter 5: Eigenvalues and
Eigenvectors
1.
Eigenvectors and Eigenvalues.
2. The
Characteristic Equation.
3.
Diagonalization.
5.
Complex Eigenvalues.
Chapter 6: Orthogonality and
Least-Squares
1.
Inner Product, Length, and Orthogonality.
2.
Orthogonal Sets.
3.
Orthogonal Projections.
4. The
Gram-Schmidt Process.