# Mount Holyoke College

# Math 211: Linear Algebra

# Syllabus

### Systems of linear equations (Chapter 1)

- Introduction. Solving of simple systems.
- Gaussian Elimination.
- Matrices and matrix operation.
- Inverse matrix.
- Elementary Matrices and a method for finding inverse matrix.

### Determinants (Chapter 2)

- Axioms. Examples of computation. Uniqueness.
- Permutations. Sign of permutation. Formula for determinant.
- Row reduction. Column reduction.
- Minors. Inverse matrix and Cramer's Rule.

### Vector spaces (Chapters 3,4)

- Vectors. Vector arithmetic. Coordinates.
**R**^{n}.
- Vector spaces. Linear combinations. Linear independence. Basis and
dimension.
- Row and column space of a matrix. Rank.

### Linear transformations (Chapters 5,6)

- Linear and non linear transformations. Examples.
- Kernel and range.
- Matrices of linear transformations. Composition of linear
transformations.
- Dependence of the choice of basis. Similarity.
- Eigenvalues and eigenvectors.