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let A be the squere matrix. then which of the following is not a symmetric matrix. 1 = A+A’ 2 = A’A 3 = AA’ 4 = A-A’

let A be the squere matrix. then which of the following is not a symmetric matrix.
1 =  A+A’
2 = A’A
3 = AA’
4 = A-A’

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
Hello student,
First of all, a symmteric matrix is one in which the transpose of the matrix equals the matrix itslef.
So, mathematically, If AT = A, then A is symmetric.
So, now consider the options one by one.
(1) A+A’
To find out whether it is symmetric or not, find its transpose.
So, (A+A’)’ = (A’)’ + A’
= A + A’
= A’ + A
Hence, it is symmetric.
(2) A’A and (3) A’A
Similarly, you can prove that both AA’ and A’A are symmetric matrcies.
(4) (A-A’)
(A-A’)’ = A’ – (A’)’
= A’ – A
= – (A-A’)
Hence, this is not a symmetric matrix,

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