This module is prepared for second year natural and computational sciences students for basic applied mathematics. This module is also important for the engineering and technology students.In this module, much emphasis is put on explanations of concepts and solving examples .By reading the module carefully, students should be able to understand the concepts introduced and know how to answer questions with justification. At the end of each chapter there is an exercise. Students are advised to do as many questions as possible.This module has five different chapters. The first chapter deals about concepts and applications of vectors. Under this chapter, vector n-space; geometric interpretation in 2-space and 3-space, orthogonal projection and application of vectors haven been discussed.The second chapter discusses on matrices and determinants .It includes discussion on operations on matrices, elementary row operations, systems of linear equations, definition of determinant, Properties of determents ,adjoint and inverse of a matrix and solving system of linear equations using Cramer¿s rule, matrix inversion and Gaussian elimination methods .