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

For the matrices `A` and `B` , `A=[2 1 3 4 1 0]` , `B=[1-1 0 2 5 0]` verify that `(A B)^T=B^T\ A^T`

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Given : `A=[(2, 1, 3),( 4, 1, 0)]` , `B=[(1,-1),( 0, 2),( 5, 0)]`
Then
AB=`[(2, 1, 3),( 4, 1, 0)] [(1,-1),( 0, 2),( 5, 0)]`
`AB=[(2+0+15,-2+2+1),(4+0+0,-4+2)]`
`AB=[(17,0),(4,-2)]`
`AB^T=[(17,4),(0,-2)].......(i)`
...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[-2 4 5] , B=[1\ \ 3\ \ -6] , verify that (A B)^T=B^T\ A^T

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

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  3. For the matrices A and B , A=[2 1 3 4 1 0] , B=[1-1 0 2 5 0] verify th...

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

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  5. 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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  6. If A=[cosalphasinalpha-sinalphacosalpha] , then verify that A^T\ A=I2 ...

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

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

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

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  10. If the matrix A=[0a3 2b-1c1 0] is skew-symmetric, find the values o...

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

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

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

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

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  15. Let A and B be symmetric matrices of same order. Then A+B is a symmetr...

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

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

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

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

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

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