Question-1 :-
Find the transpose of each of the following matrices:
(i)![]()
(ii)![]()
(iii)![]()
Question-2 :-
(i) (A + B)′ = A′ + B′,
(ii) (A – B)′ = A′ – B′
(i)![]()
(ii)![]()
Question-3 :-
(i) (A + B)′ = A′ + B′,
(ii) (A – B)′ = A′ – B′
(i)![]()
(ii)![]()
Question-4 :-
Question-5 :-
For the matrices A and B, verify that (AB)′ = B′A′, where
(i)![]()
(ii)![]()
Question-6 :-
(i)![]()
(ii)![]()
Question-7 :-
(i)![]()
(ii)![]()
Question-8 :-
(i) (A + A′) is a symmetric matrix
(ii) (A – A′) is a skew symmetric matrix
(i)![]()
(ii)![]()
Question-9 :-
Question-10 :-
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
(i)![]()
(ii)![]()
(iii)![]()
(iv)![]()
Question-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
A and B are symmetric matrices, therefore, we have: A' = A, B' = B .........(I) Consider (AB - BA)' = (AB)' - (BA)' [(A - B)' = A' - B'] = B'A' - A'B' [(AB)' = B'A'] = AB - BA [By equation I] Thus, (AB − BA) is a skew-symmetric matrix. The correct answer is A.
Question-12 :-
(A) π/6 (B) π/3 (C) π (D) 3π/2
The correct answer is B.