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Learning Outcomes for 3450:312 Linear Algebra
Students are expected to be able to
- Determine if a set of vectors is linearly independent
- Represent systems of linear equations using matrices and solve such systems
- Find bases and dimensions of vector spaces
- Determine properties of matrix transformations
- Find eigenvalues and eigenvectors for given matrix
- Write elementary proofs
- Topical Outline
- Systems of Linear Equations
- Matrices and Elementary Row Operations
- Matrix Algebra
- The Inverse of a Square Matrix
- Matrix Equations
- Elementary Matrices and LU Factorization
- Vectors in Rn
- Linear Combinations
- Linear Independence
- Definition of a Vector Space
- Subspaces
- Basis and Dimension
- Linear Transformations
- The Null Space and Range
- Isomorphisms
- Matrix Representation of a Linear Transformation
- Similarity
- Eigenvalues and Eigenvectors
- Diagonalization