Chapter 1

Matrices and Determinants

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns

Types of Matrices

(1) Square Matrix
If the number of rows a matrix are equal to the number of its columns ie., if m = n, it is called a
square matrix.
Matrix A is a square matrix as there are only 2 rows and 2 columns. It is called a square matrix of
2×2. Similarly B is a square matrix of 3×3.

(2) Diagonat Marix
A squarc martix is called a diagonal matrix when all its elements except the principal diagonal
elements are zero.

(3) Identify Matrix of Unit Matrix
A square matrix whose principal diagonal are 1 and all elements above and below the principal
diagonal are zero is known as an Identity matrix.

(4) Scalar Matrix:
If the diagonal elements of a matrix are equal it is called a Scalar matrix.

Algebra of Matrices

(1) Addition of Matrices:

(2) Subtraction of Matrices:

(3) Multiplication of a matrix by a Scalar

Properties Of Matrix Multiplication :

Transpose of a Matrix

Properties of the Transpose of a Matrix :

Symmetric and Skew, Symmetric Matrices.

Determinants

In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix.