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## Matrices

In this chapter we shall study matrices in detail. Apart from studying el-ementary operations on matrices, namely addition and multiplication, to find the product and inverse of large order matrices, the technique of partitioning is explained. Properties of special types of matrices have been discussed. We end with a study of eigen values and eigen vectors of square matrices.

#### 11.1 Matrix of Numbers

We begin by defining a matrix of numbers as follows:

Definition 11.1.    A m x n matrix A is a rectangular array of ran numbers arranged in m horizontal rows and n vertical columns:

Notation Matrices are generally denoted by ...

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