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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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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Show that all positive integral powers of a symmetric matrix are sy...

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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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  6. If the matrix A=[[5 ,2,x], [y, z,-3], [4,t,-7]] is a symmetric matrix,...

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  7. Let A=|(3, 2, 7),( 1, 4, 3),(-2, 5, 8)| . Find matrices X and Y such t...

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  8. Express the matrix A=[[4, 2,-1], [3 ,5, 7], [1,-2 ,1]] as the sum of a...

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

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

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  11. Express the matrix A=[[3,-2,-4], [3,-2,-5],[-1, 1, 2]] as the sum of a...

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  12. If A is an mxxn matrix and B is nxxp matrix does A B exist? If yes, wr...

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

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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 A A^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=[[i,0], [0,i]] , write A^2 .

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  19. If A=[[cosx,sinx],[-sinx,cosx]] , when A + A^T= I find x satisfying 0 ...

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

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