MAT 141E - Linear Algebra I

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, inverse of a matrices, the properties of the determinant function..
4.To teach vector spaces, subspaces, span of a set, linear independency of a set, basis, the
coordinates of a vector, and the dimension .

Course Description

Systems of linear equations and matrices; matrix algebra, special types of matrices, elementary
row and column operations, echelon form, elementary matrices, inverses, equivalent matrices.
Solutions of systems of linear equations. Determinants; properties of determinants, cofactor and
adjoint of a matrix, derivation of inverse matrix, Cramer's rule. Vector Spaces; def ini t ion of vector
spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis and
isomorphisms, rank of a matrix.