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

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

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To prove that the matrix \( A - A^T \) is skew-symmetric, we will follow these steps: ### Step 1: Define the matrix \( A \) Given the matrix: \[ A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \] ...
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Show that positive odd integral powers of a skew-symmetric matrix are ...

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

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

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

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

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  6. Let A=[3 2 7 1 4 3-2 5 8] . Find matrices X and Y such that X+Y=A , wh...

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

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

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

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  10. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

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

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

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

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

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

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

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

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

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  20. If [(1, 0),(y,5)]+2[(x,0),( 1,-2)]=I , where I is 2xx2 unit matrix. Fi...

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