Matrices are very important and indispensable in handling system of linear equations which arise as mathematical models of real-world problems.

Applications
of Matrices and Determinants

*“The greatest mathematicians, as Archimedes,
Newton, and Gauss, *

*always united theory and applications in equal
measure.”*

**-Felix
Klein**

Matrices are very important and indispensable in handling system
of linear equations which arise as mathematical models of real-world problems.
Mathematicians Gauss, Jordan, Cayley, and Hamilton have developed the theory of
matrices which has been used in investigating solutions of systems of linear
equations.

In this chapter, we present some applications of matrices in
solving system of linear equations. To be specific, we study four methods,
namely (i) Matrix
inversion method, (ii)
Cramer’s rule (iii) Gaussian
elimination method, and (iv) Rank method. Before knowing these methods, we
introduce the following: (i) Inverse of a non-singular square matrix, (ii) Rank
of a matrix, (iii) Elementary row and column transformations, and
(iv) Consistency of system of linear equations.

Upon
completion of this chapter, students will be able to

● Demonstrate a few fundamental tools for
solving systems of linear equations:

̵ Adjoint of a square matrix

̵ Inverse of a non-singular matrix

̵ Elementary row and column operations

̵ Row-echelon form

̵ Rank of a matrix

● Use row operations to find the inverse of
a non-singular matrix

● Illustrate the following techniques in
solving system of linear equations by

̵ Matrix inversion method

̵ Cramer’s rule

̵ Gaussian elimination method

● Test the consistency of system of
non-homogeneous linear equations

● Test for non-trivial solution of system of
homogeneous linear equations

Tags : Applications of Matrices and Determinants , 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Introduction | Applications of Matrices and Determinants

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