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For two matrices A and B , verify that (...

For two matrices `A` and `B` , verify that `(A B)^T=B^T\ A^T` , where `A=[[1 ,3 ] , [2 ,4]]` , `B=[[1 , 4 ] , [ 2 ,5] ]`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[[2 , 4 ,-1] , [-1 , 0 , 2]] , B=[[3 , 4], [-1 ,2] , [ 2 ,1]] , ...

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  2. For the matrices A and B , A=[[2 ,1 ,3 ] , [4 ,1 ,0 ]] , B=[[1 , -1] ,...

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  3. For two matrices A and B , verify that (A B)^T=B^T\ A^T , where A=[[1 ...

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  4. If A^T=[3 4-1 2 0 1] and B=[-1 2 1 1 2 3] , find A^T-B^T .

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  5. If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] , then verify that A^T...

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  6. If A=[[sinalpha,cosalpha],[-cosalpha,sinalpha]], verify that A^T A=I2

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  7. Let li,mi,ni; i=1,2,3 be the direction cosines of three mutually perpe...

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  8. Show that the elements on the main diagonal of a skew-symmetric mat...

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  9. If the matrix A=[[0,a,-3],[2,0,-1],[b,1,0]] is skew-symmetric, find ...

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  10. Let A be a square matrix. Then prove that (i) A + A^T is a symmetric m...

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  11. Prove that every square matrix can be uniquely expressed as the sum of...

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  12. If A and B are symmetric matrices, then show that A B is symmetric i...

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  13. Show that the matrix B^T\ A B is symmetric or skew-symmetric accord...

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  14. Let A and B be symmetric matrices of same order. Then AB-BA is a skew ...

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  15. Express the matrix A=|(3, 2 ,3),(4,5 ,3),( 2, 4,5)| as the sum of a ...

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  16. Show that all positive integral powers of a symmetric matrix are sy...

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  17. Show that positive odd integral powers of a skew-symmetric matrix are ...

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

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

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

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