This page contains some links to pages with material relevant to the elementary linear algebra course. You will also find links to Mathematica notebooks which you can download and modify for further exploration.

• Section 02 current semester syllabus
• Official department syllabus
• Solutions to homework exercises.
• Old tests and their answers.
• Systems of linear equations.
• Gaussian elimination.
• Matrix operations.
• Rules of matrix arithmetic.
• Elementary matrices.
• Properties of invertible matrices.
• Diagonal, triangular, and symmetric matrices.
• The determinant function.
• Evaluating determinants using row reduction.
• Properties of the determinant.
• Cofactor expansions and Cramer's Rule.
• Euclidean n-Space
• Linear transformations from Rⁿ to R^m
• Properties of linear transformations from Rⁿ to R^m
• Real vector spaces
• Subspaces of vector spaces.
• Linear independence of vectors in a vector space.
• Basis and dimension of a vector space.
• The row space, column space, and nullspace of a matrix.
• The rank and nullity of a matrix.
• The generalized inner product.
• Angle and orthogonality in inner product spaces.
• Orthonormal bases, the Gram-Schmidt process, and the QR-decomposition.
• Orthogonal matrices and change of basis.
• Eigenvalues and eigenvectors.
• Diagonalization of matrices.
• Orthogonal Diagonalization of matrices.
• An introduction to generalized linear transformations.
• Kernel and range of a generalized linear transformation.
• An introduction to inverse linear transformations.
• Matrix representations of general linear transformations.
• An introduction to similarity.