MAT 143E - Linear Algebra

Course Objectives

1. To teach matrix algebra and system of linear equations.
2. To teach how to solve a system of linear equations
3. To teach invertible matrices and the properties of the determinant.
4. To teach vector spaces, subspaces, span of a set, linear independence, basis, coordinates of a
vector, and the dimension.
5. To teach the concept of inner product, inner product space and diagonalization methods.
6. To teach linear transformations and their matrix representations.

Course Description

Linear Equations and Matrices, Systems of Linear Equations, Matrices, Matrix algebra, Special Types
of Matrices, Solving Linear Systems, Echelon Form a Matrix, Solutions of Systems of Linear
Equations, Elementary Matrices, Inverse of a Matrix. Determinants, Definition, Properties of
Determinants, Cofactor and Adjoint of a Matrix, Derivation of Inverse Matrix. Cramer's Rule. Real
Vector Spaces, Definition of Vector Spaces, Subspaces, Linear Independence, Bases and Dimension,
Coordinates, Change of Basis and Rank of a Matrix. Inner Product Spaces, Standard Inner Product,
Orthogonal Subspaces, Orthogonal Complement of a Subspace, Inner Product Spaces, Cauchy-
Schwarz Inequality, Orthogonal Basis, Gram-Schmidt Method. Linear Transformations and Matrices;
Definition of a Linear Transformations, The Kernel and Range of a Linear Transformation, Matrix
Representations of a Linear Transformations.