Express the following matrices as the sum of a symmetric and a skew symmetric
matrix:
Rationalised 2023-24
 68
MATHEMATICS
(i)
3
5
1
1



−


(ii)
6
2
2
2
3
1
2
1
3
−




−
−




−


(iii)
3
3
1
2
2
1
4
5
2
−




−
−




−
−


(iv)
1
5
1
2




−

Choose the correct answer in the Exercises 11 and 12 11 If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix
12 If 
cos
sin
A
,
sin
cos
α
−
α


= 

α
α


and  A + A′ = I, then the value of α is
(A) 6
π
(B) 3
π
(C) π
(D) 3
2
π
3