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Find the transpose of each of the following matrices:
(i) 
(ii) 
(iii) 
(i) 
(ii) 
(iii) 
If 
and
, then verify that
(i) 
(ii) 
(i) It is known that
Therefore, we have:
(ii)
(i) Show that the matrix 
is a symmetric matrix
(ii) Show that the matrix 
is a skew symmetric matrix.
(i) Transpose of a matrix is equal to original matrix,then it is symmetric.
Hence, A is a symmetric matrix.
(ii) If it is equal to negetive,then it is skew symmetric matrix. Diagonal elements of this matrix are zero.
Hence, A is a skew-symmetric matrix.
For the matrix
, verify that
(i) 
is a symmetric matrix
(ii) 
is a skew symmetric matrix
(i) 
Hence, 
is a symmetric matrix.
(ii) 
Hence, 
is a skew-symmetric matrix.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
(i) 
(ii) 
(iii) 
(iv) 
(i)
Thus, 
is a symmetric matrix.
Thus, 
is a skew-symmetric matrix.
Representing A as the sum of P and Q:
(ii)
Thus, is a symmetric matrix.
Thus, is a skew-symmetric matrix.
Representing A as the sum of P and Q:
(iii)
Thus, is a symmetric matrix.
Thus, is a skew-symmetric matrix.
Representing A as the sum of P and Q:
(iv)
Thus, is a symmetric matrix.
Thus, is a skew-symmetric matrix.
Representing A as the sum of P and Q:
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
The correct answer is A.
A and B are symmetric matrices, therefore, we have:
Thus, (AB − BA) is a skew-symmetric matrix.
If
, then
, if the value of α is
A. 
B. 
C. π D. 
The correct answer is B.
Comparing the corresponding elements of the two matrices, we have:
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and
, when 
and
, then verify that
and
, then find 
where
, then verify that 
, then verify that 
