Also, let
Q =
1
5
0
2
2
0
1
5
1
1
1
(B – B )
1
0
6
0
3
2
2
2
5
6
0
5
3
0
2
−
−




−
−








′ =
=






−






−




Rationalised 2023-24
 66
MATHEMATICS
Then
Q′ =
1
5
0
2
3
1
0
3
Q
52
3
0
2






−
−
= −




−





Thus
Q = 1 (B – B )
2
′  is a skew symmetric matrix Now
3
3
1
5
2
0
2
2
2
2
2
2
4
3
1
P + Q
3
1
0
3
1
3
4
B
2
2
1
2
3
3
5
1
3
3
0
2
2
−
−
−
−








−
−






−






=
+
= −
=








−
−






−



−
−








Thus, B is represented as the sum of a symmetric and a skew symmetric matrix EXERCISE 3 3
1