MATH- 244, Linear Algebra

Course Contents

Matrices: Matrices and matrix operations; elementary row and column operations; inverse of a matrix; special matrices.
Determinants: Definition of determinant of a matrix; evaluation of a determinant; properties of determinants; adjoint of a matrix and its properties.
Linear Systems: Systems of linear equations; Gauss and Gauss – Jordan elimination methods; homogeneous systems of linear equations; Cramer’s Rule.
Vector Spaces: Definition of a vector space and examples; subspaces; linear combinations and linear span of a sets of vectors; linear dependence and linear independence of a set of vectors; basis and dimension of a vector space; coordinates of a vector with respect to a basis; change of basis; rank and nullity of a matrix.
Inner Product Spaces: Definition of inner product and inner product space with examples; orthogonal and orthonormal sets of vectors; orthonormal basis; Gram-Schmidt orthonormalization process.
Linear Transformations: Definition of a linear transformation and examples; basic properties of linear transformations; kernel and image spaces of a linear transformation; matrix of linear transformation.
Eigenvalues, Eigenvectors and Diagonalization: Eigenvalues and eigenvectors of a matrix; diagonalization of a matrix.

Recommended Book: “Elementary Linear Algebra (Applications Version)” by Howard Anton and Chris Rorres, 11th Edition, Wiley, USA, 2014.