Question

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⏩What do you mean by symmetric matrix and skew symmetric matrix??Explain with suitable examples..
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Answer 1

Step-by-step explanation:

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal.

A scalar multiple of a skew-symmetric matrix is skew-symmetric. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore also its trace.

Answer 2

Symmetric Matrix:-

»» A square matrix $\sf{[a_{ij}]}$ is said to be symmetric matrix if A' = A, that is, $\sf{[a_{ij}]}$ = $\sf{[a_{ji}]}$ for all possible values of i and j

For example A = [√3 2 3, 2 -1.5 -1, 3 -1 1] of order 3×3 is a symmetric matrix as A' = A

Skew Symmetric Matrix:-

»» A square matrix A = $\sf{[a_{ij}]}$ is said to be skew symmetric matrix if A' = -A, that is $\sf{[a_{ji}]}$ = $\sf{[-a_{ij}]}$ for all possible values of i and j. Now, if we put i = j, we have $\sf{[a_{ii}]}$ = $\sf{[-a_{ii}]}$. Therefore $\sf{[2a_{ii}]}$ = 0 or $\sf{[a_{ii}]}$ = 0 for all i's.

This means that all the diagonal elements of a skew symmetric matrix are zero.