Inverse of Matrices and Solution of Linear Equations

Dr. Jagjit Singh

Govt. College Bhoranj (Tarkwari), District Hamirpur (H.P.)

*Corresponding Author Email: jagjitsinghpatial@gmail.co

ABSTRACT:

In this paper, an algebraic method has been given to find the inverse of a non- singular square matrix and on the basis of this method , a short cut to find inverse of a non- singular square matrix has been given. A method is given to solve a system of non- homogeneous linear equations in n unknowns by reducing it into system of non-homogeneous linear equations in n–1 unknowns.

KEY WORDS: inverse, co-factor, adjoint, non- singular, linear, non-homogeneous.

1. INTRODUCTION:

We generally use the method of minors and co-factors to find the adjoint and inverse of a square matrix. Here, linear algebraic equations will be formed and then by using determinant and Cramer’s rule, the adjoint and inverse of a matrix will be calculated. A short cut method to find the adjoint and inverse of a non-singular matrix will also be presented. Detailed studies on the properties and problems of matrices can be had in the books of following authors: David C. Lay (2002), Fuzhen Zhang (2011), Richard Bronson (1989) and Seymour Lipschutz, Marc Lipson (2008).

REFERENCES:

1. David C. Lay, Linear Algebra and its Applications, Pearson Education India (2002).

2. Fuzhen Zhang, Matrix Theory: Basic Results and Techniques, Springer (2011)

3. Richard Bronson, Schaum’s Outline of Theory and Problems of Matrix Operations, McGraw-hill (1989).

4. Seymour Lipschutz, Marc Lipson, Schaum’s Outlines: Linear Algebra, McGraw-Hill Professional (2008).

Received on 16.08.2016 Accepted on 01.09.2016

Int. J. Tech. 2016; 6(2): 63-70

DOI: 10.5958/2231-3915.2016.00010.9