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Let A=[1-1 0 2 1 3 1 2 1]a n dB=[1 2 3 2...

Let `A=[1-1 0 2 1 3 1 2 1]a n dB=[1 2 3 2 1 3 0 1 1]dot` Find `A^T ,B^T` and verify that `(A+B)^T=A^T+B^T` (ii) `(A B)^T=B^T A^T` `(2A)^T=2A^T`

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Let A=[(2,-3),(-7, 5)] and B=[(1, 0),( 2,-4)] , verify that (2A)^T=2A^...

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  2. If A=[[3] , [ 5] , [2] ] and B=[1\ \ 0\ \ 4] , verify that (A B)^T=B^T...

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  3. Let A=[1-1 0 2 1 3 1 2 1]a n dB=[1 2 3 2 1 3 0 1 1]dot Find A^T ,B^T a...

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  4. If A=[[-2],[4], [5]], B=[[1 ,3,-6]], verify that (A B)' = B'A'.

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  5. If A=[[2 , 4 ,-1] , [-1 , 0 , 2]] , B=[[3 , 4], [-1 ,2] , [ 2 ,1]] , ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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