Slide 1 : 11. Equal Matrices :
Two matrices A and B are said to be equal matrices , written as A = B, if
i) They both are of the same order.
ii) The elements in the corresponding places
of two matrices are same.
e.g. If A = and B =
Then A = B. 5 0 2
1 3 8
4 2 2 5 0 2
1 3 8
4 2 2
Slide 2 : 12. Transpose of a Matrix :
Let A be a matrix of order m × n, then the matrix of order n × m obtained from A by interchanging the rows and columns is called as the transpose of matrix A.
It is denoted by A| or AT.
e.g. If A = then A| = 5 0 2
1 3 8
4 2 2 5 1 4
0 3 2
2 8 2
Slide 3 : 13. Symmetric Matrix :
A square matrix A is said to be symmetric if A| = A.
Thus a square matrix A = [aij] is symmetric if
aij = aji for all values of i and j.
e.g. If A = then A| =
We observe that A| = A.
Therefore A is a symmetric matrix. 8 7
8 6 4
7 4 1 8 7
8 6 4
7 4 1
Slide 4 : 14. Skew - Symmetric Matrix :
A square matrix A is said to be skew-
symmetric if A| = -A.
Thus a square matrix A = [aij] is skew- symmetric if aij = -aji for all values of i and j.
Note: In a skew-symmetric matrix, for diagonal elements
aii = -aii for all i.
? aii + aii = 0
? 2 aii = 0 ? aii = 0
Slide 5 : Thus in a skew-symmetric matrix all its diagonal elements are zero
e.g. Let A =
? A| = = - A
This shows that A is a skew-symmetric matrix 0 3 -6
-3 0 8
6 -8 0 0 -3 6
3 0 -8
-6 8 0
Believe on your strength : Believe on your strength 15. Addition of Matrices:
Let there be two matrices A and B of the same order m x n. Then there sum denoted by A + B is defined to be the matrix of order m x n obtained by adding the corresponding elements of A and B.
Thus if A = [aij]m x n and B = [ bij ]m x n, then
A + B = [aij + bij]m x n [Note that we can find the sum A + B only if the matrices A and B are of the same order
i.e. if the number of rows and columns of matrix A are equal to those of matrix B.]
Believe on your strength : Believe on your strength e.g. Let
A = and B =
Then A + B = +
=
= 1 -2 4
2 3 8
7 5 6 3 2 5
2 6 3
9 0 1 1 -2 4
2 3 8
7 5 6 3 2 5
2 6 3
9 0 1 1 + 3 -2 + 2 4 + 5
2 + 2 3 + 6 8 + 3
7 + 9 5 + 0 6 + 1 4 0 9
4 9 11
16 5 7
Slide 8 : = = 7 7 4 5 0 7 5 7 Ex.2
Slide 9 : Ex.1 Ex.2 + = 3 -2 8 10 8 -1 8 5 9 Ex.3 + = 9 7 16 4 10 12