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A matrix which is both symmetric as w...

A matrix which is both symmetric as well as skew-symmetric is a null matrix.

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If a matrix is both symmetric and skew symmetric matrix, then
`A` is symmetric matrix
`Rightarrow aij=aji`
`A` is a skew symmetric matrix
`Rightarrow aij=-aji`
If `aij=aji=-aji`
`Rightarrow aij=0 Rightarrow aji=-aji`
Hence `A` is a zero or null matrix.
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  2. Show that positive odd integral powers of a skew-symmetric matrix are ...

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  3. A matrix which is both symmetric as well as skew-symmetric is a nul...

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  4. If A=[2 3 4 5] , prove that A-A^T is a skew-symmetric matrix.

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  5. If A=[3-4 1-1] , show that A-A^T is a skew symmetric matrix.

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  9. Define a symmetric matrix. Prove that for A=[2 4 5 6] , A+A^T is a ...

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  10. Express the matrix A=[3-4 1-1] as the sum of a symmetric and a skew-sy...

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  13. If A=[2 1 4 4 1 5] and B=[3-1 2 2 1 3] . Write the orders of A B and B...

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  14. If A=[4 3 1 2] and B=[-4 3] , write A B .

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  15. If A=[1 2 3] , write AA^T .

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  16. Give an example of two non-zero 2xx2 matrices A and B such that A B...

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  17. If A=[2 3 5 7] , find A+A^T .

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  18. If A=[i0 0i] , write A^2 .

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  19. If A=[(cosx,sinx),(-sinx,cosx)] , find x satisfying 0<x<pi/2 when A+A^...

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  20. If A=[(cosx,-sinx),(sinx,cosx)] , find AA^T

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