ABSTRACT
Advances in technology and sophisticated computers opened up a galaxy of problems that can be studied numerically. Any challenging problem in space exploration, missile technology, genetic coding or the age old transportation problem involve a whole bunch of equations (obtained through prior knowledge) involving a large number of variables. These equations, if expressed adroitly as a linear system, can be reduced to the study of matrices. In this chapter a linear system of equations is introduced in Section 2.2 and the concept of rank of a matrix which gives a very good understanding of the system of equations, is discussed in Section 2.3. The row echelon form and the normal form that help finding the rank of a matrix are described in Section 2.4. The theory of linear system of homogeneous and non-homogeneous equations form the content of Section 2.5. Cayley Hamilton theorem is stated and its use in finding the inverse of a matrix is dealt in Section 2.6. The Eigen values, and Eigen vectors, along with diagonalizationss of a matrix are studied in Section 2.7. Section 2.8 deals with singular values and singular vectors and the quadratic forms are dealt in Section 2.9.
