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. Rⁿ.
• 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.