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Unit 3: Matrix

3.2 Equality of Matrices Notes

Two matrices A and B are said to be equal if they are of the same order and the corresponding
elements of A and B are equal:

1 2 3 1 2 3
Example: (1) A , B
8 7 4 8 7 4
2 3 2 3
The orders are same and the corresponding elements are equal.
A . B

x 2 1 2
(2) If A and B then
0 y 0 4
2 2
A B x 1 and y . 4

3.3 Types of Matrices

1. Rectangular matrix: A matrix of order m n is called a rectangular matrix.

1 2 1
Example: A is a rectangular matrix.
4 7 0
2 3
2. Square matrix: A matrix in which the number of rows is equal to the number of columns
(i.e., m m matrix) is called square matrix.

2 6 11
1 4
Example: A B 5 0 8
7 0
2 2 7 4 1
3 3
3. Diagonal matrix: A square matrix in which all the elements except the principal diagonal
elements are zero, is called a diagonal matrix.

4 0 0
2 0
Example: A , B 0 1 0 are diagonal matrices.
0 1
0 0 8

Notes If A = [a ] is a sq matrix of order n, then elements entries a , a … a are said to
ij 11 22 nn
1 3 1
constitute diagonal of the matrix A. Thus of A = 2 4 1 , Them elements of the
3 5 6
diagonal of A are 1, 4, 6.

4. Scalar matrix: A diagonal matrix in which all the principal diagonal elements are equal,
is called a scalar matrix.

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