MATH 320 LINEAR ALGEBRA

Course Syllabus

1. Matrices and Linear Systems

a. Algebraic Solution for Linear Systems

b. Matrix Notation and Operations

c. Row Reduction of Matrices and Solutions to Linear Systems d. Inverses of Matrices.

2. Determinants

a. Definition and Computational Schemes

b. Properties of Determinants

c. Adjoint Matrix

3. Vector Spaces

a. Geometric Examples

b. Definition and Basic Properties

c. Subspaces

d. Linear Dependence and Independence

e. Bases and Dimension

4. Linear Transformations

a. Definition and Basic Properties

b. Kernel of a Linear Transformation

c. Matrix Associated with a Linear Transformation

d. Change of Basis Matrix

e. Orthonormal Bases

f. Least Squares Approximation

5. Eigenvalues and Eigenvectors

a. Definition and Basic Properties

b. Computation

c. Similar Matrices

d. Diagonal Matrices

Prerequisites: MATH 220

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